{"name": "代数几何学", "children": [{"name": "交换环", "children": [{"name": "I进拓扑", "en": "I-adic topology", "superfield": "数学"}, {"name": "p基", "en": "p-basis", "superfield": "数学"}, {"name": "不可约元", "en": "irreducible element", "superfield": "数学"}, {"name": "主理想整环", "en": "principal ideal domain", "superfield": "数学"}, {"name": "乘性子集", "en": "multiplicative subset", "superfield": "数学"}, {"name": "乘法交换律", "en": "commutative law of multiplication", "superfield": "数学"}, {"name": "乘法消去律", "en": "cancellation law for multiplication", "superfield": "数学"}, {"name": "交换A代数", "en": "commutative A-algebra", "superfield": "数学"}, {"name": "交换代数", "en": "commutative algebra", "superfield": "数学"}, {"name": "交换环", "en": "commutative ring", "superfield": "数学"}, {"name": "亨泽尔环", "en": "Henselian ring", "superfield": "数学"}, {"name": "优环", "en": "excellent ring", "superfield": "数学"}, {"name": "克鲁尔环", "en": "Krull ring", "superfield": "数学"}, {"name": "克鲁尔维数", "en": "Krull dimension", "superfield": "数学"}, {"name": "准素分解", "en": "primary decomposition", "superfield": "数学"}, {"name": "准素分量", "en": "primary component", "superfield": "数学"}, {"name": "准素理想", "en": "primary ideal", "superfield": "数学"}, {"name": "分式域", "en": "quotient field", "superfield": "数学"}, {"name": "分式环", "en": "ring of fractions", "superfield": "数学"}, {"name": "分次同态", "en": "graded homomorphism", "superfield": "数学"}]}, {"name": "代数K理论", "children": [{"name": "代数K理论", "en": "algebraic K theory", "superfield": "数学"}, {"name": "保积函子", "en": "product-preserving functor", "superfield": "数学"}, {"name": "共尾保积函子", "en": "cofinal product-preserving functor", "superfield": "数学"}, {"name": "可逆模", "en": "invertible module", "superfield": "数学"}, {"name": "带积合成范畴", "en": "category with product and com- position", "superfield": "数学"}, {"name": "带积范畴", "en": "category with product", "superfield": "数学"}, {"name": "常数秩模", "en": "module of constant rank", "superfield": "数学"}, {"name": "怀特黑德群", "en": "Whitehead group", "superfield": "数学"}, {"name": "施坦贝格关系", "en": "Steinberg relations", "superfield": "数学"}, {"name": "施坦贝格群", "en": "Steinberg group", "superfield": "数学"}, {"name": "格罗滕迪克群", "en": "Grothendieck group", "superfield": "数学"}, {"name": "环的怀特黑德群", "en": "Whitehead group of a ring", "superfield": "数学"}, {"name": "环的施坦贝格群", "en": "Steinberg group of a ring", "superfield": "数学"}, {"name": "环的格罗滕迪克群", "en": "Grothendieck group of a ring", "superfield": "数学"}, {"name": "约化格罗滕迪克群", "en": "reduced Grothendieck group", "superfield": "数学"}, {"name": "行列式映射", "en": "determinant mapping", "superfield": "数学"}, {"name": "连通环", "en": "connected ring", "superfield": "数学"}, {"name": "阿贝尔化函子", "en": "abelianizing functor", "superfield": "数学"}]}, {"name": "代数几何学", "children": []}, {"name": "S态射", "en": "S-morphism", "superfield": "数学"}, {"name": "S概形", "en": "S-scheme", "superfield": "数学"}, {"name": "[代数]簇", "en": "[algebraic] variety", "superfield": "数学"}, {"name": "d重嵌入", "en": "d-uple imbedding", "superfield": "数学"}, {"name": "l进上同调", "en": "l-adic cohomology", "superfield": "数学"}, {"name": "三重点", "en": "triple point", "superfield": "数学"}, {"name": "不可分态射", "en": "inseparable morphism", "superfield": "数学"}, {"name": "不可约曲线", "en": "irreducible curve", "superfield": "数学"}, {"name": "不可约概形", "en": "irreducible scheme", "superfield": "数学"}, {"name": "丰富可逆层", "en": "ample invertible sheaf", "superfield": "数学"}, {"name": "丰富完全线性系", "en": "ample complete linear system", "superfield": "数学"}, {"name": "丰富除子", "en": "ample divisor", "superfield": "数学"}, {"name": "二次变换", "en": "quadratic transformation", "superfield": "数学"}, {"name": "二重切线", "en": "double tangent", "superfield": "数学"}, {"name": "亏格", "en": "genus", "superfield": "数学"}, {"name": "交重数", "en": "intersection multiplicity", "superfield": "数学"}, {"name": "代数几何[学]", "en": "algebraic geometry", "superfield": "数学"}, {"name": "代数曲线", "en": "algebraic curve", "superfield": "数学"}, {"name": "代数等价", "en": "algebraically equivalence", "superfield": "数学"}, {"name": "代数闭链", "en": "algebraic cycle", "superfield": "数学"}, {"name": "代数群", "children": [{"name": "G等价态射", "en": "G-equivalent morphism", "superfield": "数学"}, {"name": "d群", "en": "d-group", "superfield": "数学"}, {"name": "一维群", "en": "one dimensional group", "superfield": "数学"}, {"name": "代数变换空间", "en": "algebraic transformation space", "superfield": "数学"}, {"name": "代数子群", "en": "algebraic subgroup", "superfield": "数学"}, {"name": "代数的李代数", "en": "algebraic Lie algebra", "superfield": "数学"}, {"name": "代数群", "en": "algebraic group", "superfield": "数学"}, {"name": "代数群的外尔群", "en": "Weyl group of algebraic group", "superfield": "数学"}, {"name": "代数群的有理表示", "en": "rational representation of algebraic group", "superfield": "数学"}, {"name": "代数群的李代数", "en": "Lie algebra of an algebraic group", "superfield": "数学"}, {"name": "代数群的根[基]", "en": "radical of algebraic group", "superfield": "数学"}, {"name": "代数群的特征[标]", "en": "character of algebraic group", "superfield": "数学"}, {"name": "代数群的秩", "en": "rank of algebraic group", "superfield": "数学"}, {"name": "仿射代数群", "en": "affine algebraic group", "superfield": "数学"}, {"name": "仿射群的线性化", "en": "linearization of affine groups", "superfield": "数学"}, {"name": "典范态射", "en": "canonical morphism", "superfield": "数学"}, {"name": "函数平移", "en": "translation of functions", "superfield": "数学"}, {"name": "半单代数群", "en": "semi-simple algebraic group", "superfield": "数学"}, {"name": "半单元", "en": "semi-simple element", "superfield": "数学"}, {"name": "半单秩", "en": "semi-simple rank", "superfield": "数学"}]}, {"name": "同调代数", "children": [{"name": "上同调", "en": "cohomology", "superfield": "数学"}, {"name": "上同调平凡模", "en": "cohomologically trivial module", "superfield": "数学"}, {"name": "上同调模", "en": "cohomology module", "superfield": "数学"}, {"name": "上同调类", "en": "cohomology class", "superfield": "数学"}, {"name": "上同调群", "en": "cohomology group", "superfield": "数学"}, {"name": "上诱导模", "en": "coinduced module", "superfield": "数学"}, {"name": "上链复形", "en": "cochain complex", "superfield": "数学"}, {"name": "上闭链", "en": "cocycle", "superfield": "数学"}, {"name": "主叉同态", "en": "principal crossed homomorphism", "superfield": "数学"}, {"name": "二重复形", "en": "double complex", "superfield": "数学"}, {"name": "交换图表", "en": "commutative diagram", "superfield": "数学"}, {"name": "伽罗瓦上同调", "en": "Galois cohomology", "superfield": "数学"}, {"name": "内射分解", "en": "injective resolution", "superfield": "数学"}, {"name": "函子Ext", "en": "functor Ext", "superfield": "数学"}, {"name": "函子Tor", "en": "functor Tor", "superfield": "数学"}, {"name": "半单李代数的上同调", "en": "cohomology of semi-simple Lie algebras", "superfield": "数学"}, {"name": "叉同态", "en": "crossed homomorphism", "superfield": "数学"}, {"name": "可裂短正合[序]列", "en": "splitting short exact sequence", "superfield": "数学"}, {"name": "右导出函子", "en": "right derived functor", "superfield": "数学"}, {"name": "右正合函子", "en": "right exact functor", "superfield": "数学"}]}, {"name": "型", "children": [{"name": "不定二次型", "en": "indefinite quadratic form", "superfield": "数学"}, {"name": "乘性二次型", "en": "multiplicative quadratic form", "superfield": "数学"}, {"name": "二次型", "en": "quadratic form", "superfield": "数学"}, {"name": "二次型的判别式", "en": "discriminant of quadratic form", "superfield": "数学"}, {"name": "二次型的哈塞不变量", "en": "Hasse invariant of a quadratic form", "superfield": "数学"}, {"name": "二次型的矩阵", "en": "matrix of quadratic form", "superfield": "数学"}, {"name": "二次型的秩", "en": "rank of quadratic form", "superfield": "数学"}, {"name": "二次型的等价", "en": "equivalence of quadratic forms", "superfield": "数学"}, {"name": "二次映射", "en": "quadratic mapping", "superfield": "数学"}, {"name": "二次空间", "en": "quadratic space", "superfield": "数学"}, {"name": "二次空间的根", "en": "radical of a quadratic space", "superfield": "数学"}, {"name": "二次空间的格", "en": "lattice in a quadratic space", "superfield": "数学"}, {"name": "交错化子", "en": "alternizer", "superfield": "数学"}, {"name": "交错双线性型", "en": "alternate bilinear form", "superfield": "数学"}, {"name": 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"polynomial of one indeterminate", "superfield": "数学"}, {"name": "一元多项式的分裂域", "en": "splitting field of a polynomial in an indeterminate", "superfield": "数学"}, {"name": "一元多项式的判别式", "en": "discriminant of a polynomial in one unknown", "superfield": "数学"}, {"name": "一般方程", "en": "general equation", "superfield": "数学"}, {"name": "三次方程", "en": "cubic equation", "superfield": "数学"}, {"name": "三重根", "en": "triple root", "superfield": "数学"}, {"name": "三项式", "en": "trinomial", "superfield": "数学"}, {"name": "三项方程", "en": "trinomial equation", "superfield": "数学"}, {"name": "不可分扩张", "en": "inseparable extension", "superfield": "数学"}, {"name": "不可分次数", "en": "inseparable degree", "superfield": "数学"}, {"name": "不可约多项式", "en": "irreducible polynomial", "superfield": "数学"}, {"name": "不可约方程", "en": "irreducible equation", "superfield": "数学"}, {"name": "二进域", "en": "dyadic field", "superfield": "数学"}]}, {"name": "拓扑群", "children": [{"name": "T2拓扑空间的基本群", "en": "fundamental group of T2 topo- logical space", "superfield": "数学"}, {"name": "T2拓扑群", "en": "T2-topological group", "superfield": "数学"}, {"name": "T2拓扑群的完全化", "en": "completion of T2 topological group", "superfield": "数学"}, {"name": "不连续变换群", "en": "discontinuous group of trans- formations", "superfield": "数学"}, {"name": "全不连通紧群", "en": "totally disconnected compact group", "superfield": "数学"}, {"name": "初等拓扑阿贝尔群", "en": "elementary topological Abelian group", "superfield": "数学"}, {"name": "完全的拓扑群", "en": "complete topological group", "superfield": "数学"}, {"name": "实数加法群", "en": "additive group of real numbers", "superfield": "数学"}, {"name": "容许T2拓扑空间", "en": "admissible T2 topological space", "superfield": "数学"}, {"name": "容许拓扑群", "en": "admissible topological group", "superfield": "数学"}, {"name": "局部单连通", "en": "locally simply connected", "superfield": "数学"}, {"name": "局部同态", "en": "local homomorphism", "superfield": "数学"}, {"name": "局部同构", "en": "locally isomorphic", "superfield": "数学"}, {"name": "局部弧连通", "en": "locally arcwise connected", "superfield": "数学"}, {"name": "局部紧群", "en": "locally compact group", "superfield": "数学"}, {"name": "局部紧群的酉表示", "en": "unitary representation of locally compact group", "superfield": "数学"}, {"name": "左一致结构", "en": "left uniformity", "superfield": "数学"}, {"name": "底群", "en": "underlying group", "superfield": "数学"}, {"name": "庞特里亚金对偶定理", "en": "Pontryagin duality theorem", "superfield": "数学"}, {"name": "开子群", "en": "open subgroup", "superfield": "数学"}]}, {"name": "李群", "children": [{"name": "p进李群", "en": "p-adic Lie group", "superfield": "数学"}, {"name": "交换李群", "en": "commutative Lie group", "superfield": "数学"}, {"name": "半单李群", "en": "semi-simple Lie group", "superfield": "数学"}, {"name": "单参数子群", "en": "one parameter subgroup", "superfield": "数学"}, {"name": "单李群", "en": "simple Lie group", "superfield": "数学"}, {"name": "单连通解析群", "en": "simply connected analytic group", "superfield": "数学"}, {"name": "可解解析群", "en": "solvable analytic group", "superfield": "数学"}, {"name": "商李群", "en": "quotient Lie group", "superfield": "数学"}, {"name": "复一般线性群", "en": "complex general linear group", "superfield": "数学"}, {"name": "复单连通解析李群", "en": "complex simply connected analytic Lie group", "superfield": "数学"}, {"name": "复李群", "en": "complex Lie group", "superfield": "数学"}, {"name": "复表示", "en": "complex representation", "superfield": "数学"}, {"name": "复解析表示", "en": "complex analytic representation", "superfield": "数学"}, {"name": "外尔特征[标]公式", "en": "Weyl character formula", "superfield": "数学"}, {"name": "外尔维数公式", "en": "Weyl dimension formula", "superfield": "数学"}, {"name": "子李群", "en": "Lie subgroup", "superfield": "数学"}, {"name": "实一般线性群", "en": "real general linear group", "superfield": "数学"}, {"name": "实李群", "en": "real Lie group", "superfield": "数学"}, {"name": "实表示", "en": "real representation", "superfield": "数学"}, {"name": "局部变换群", "en": "local transformation group", "superfield": "数学"}]}, {"name": "模论", "children": [{"name": "不可分解模", "en": "indecomposable module", "superfield": "数学"}, {"name": "主不可分解模", "en": "principal indecomposable module", "superfield": "数学"}, {"name": "余模", "en": "comodule", "superfield": "数学"}, {"name": "余模同态", "en": "comodule homomorphism", "superfield": "数学"}, {"name": "内射模", "en": "injective module", "superfield": "数学"}, {"name": "准素子模", "en": "primary submodule", "superfield": "数学"}, {"name": "升链条件", "en": "ascending chain condition", "superfield": "数学"}, {"name": "半单模", "en": "semi-simple module", "superfield": "数学"}, {"name": "单列模", "en": "uniserial module", "superfield": "数学"}, {"name": "单模", "en": "simple module", "superfield": "数学"}, {"name": "双余模", "en": "bi-comodule", "superfield": "数学"}, {"name": "双模", "en": "bimodule", "superfield": "数学"}, {"name": "双线性平衡映射", "en": "bilinear balanced map", "superfield": "数学"}, {"name": "双自同态环", "en": "biendomorphism ring", "superfield": "数学"}, {"name": "可除模", "en": "divisible module", "superfield": "数学"}, {"name": "右R模", "en": "right R-module", "superfield": "数学"}, {"name": "商模", "en": "factor module", "superfield": "数学"}, {"name": "子模", "en": "submodule", "superfield": "数学"}, {"name": "完全可约模", "en": "completely reducible module", "superfield": "数学"}, {"name": "对偶模", "en": "dual module", "superfield": "数学"}]}, {"name": "算术", "children": [{"name": "BSD猜想", "en": "Birch and Swinnerton-Dyer conjecture", "superfield": "数学"}, {"name": "l进表示", "en": "l-adic representation", "superfield": "数学"}, {"name": "p进L函数", "en": "p-adic L-function", "superfield": "数学"}, {"name": "p进形式群", "en": "p-adic formal group", "superfield": "数学"}, {"name": "p进模形式", "en": "p-adic modular form", "superfield": "数学"}, {"name": "一致分布", "en": "uniform distribution", "superfield": "数学"}, {"name": "三角和", "en": "trigonometric sum", "superfield": "数学"}, {"name": "不可公度的", "en": "incommensurable", "superfield": "数学"}, {"name": "不可约分数", "en": "irreducible fraction", "superfield": "数学"}, {"name": "不定方程", "en": "indeterminate equation", "superfield": "数学"}, {"name": "不能除尽[的]", "en": "indivisible", "superfield": "数学"}, {"name": "丢番图方程", "en": "Diophantine equation", "superfield": "数学"}, {"name": "丢番图逼近", "en": "Diophantine approximation", "superfield": "数学"}, {"name": "主理想", "en": "principal ideal", "superfield": "数学"}, {"name": "主种", "en": "principal genus", "superfield": "数学"}, {"name": "主齐性空间", "en": "principal homogeneous space", "superfield": "数学"}, {"name": "乘数", "en": "multiplicator", "superfield": "数学"}, {"name": "乘法", "en": "multiplication", "superfield": "数学"}, {"name": "二次域", "en": "quadratic field", "superfield": "数学"}, {"name": "二进制", "en": "binary system", "superfield": "数学"}]}, {"name": "线性代数", "children": [{"name": "三角形化", "en": "triangularization", "superfield": "数学"}, {"name": "三角形行列式", "en": "triangular determinant", "superfield": "数学"}, {"name": "上三角形矩阵", "en": "upper triangular matrix", "superfield": "数学"}, {"name": "不变因子", "en": "invariant divisor", "superfield": "数学"}, {"name": "不变子空间", "en": "invariant subspace", 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"结合环", "children": [{"name": "PI代数", "en": "algebra with polynomial identities", "superfield": "数学"}, {"name": "[双边]理想", "en": "[two-sided] ideal", "superfield": "数学"}, {"name": "中心代数", "en": "central algebra", "superfield": "数学"}, {"name": "中心单代数的指数", "en": "exponent of a central simple algebra", "superfield": "数学"}, {"name": "中心单代数的次数", "en": "degree of a central simple algebra", "superfield": "数学"}, {"name": "主幂等元", "en": "principal idempotent element", "superfield": "数学"}, {"name": "乘法结合律", "en": "associative law of multiplication", "superfield": "数学"}, {"name": "交换律", "en": "commutative law", "superfield": "数学"}, {"name": "代数同态", "en": "algebra homomorphism", "superfield": "数学"}, {"name": "代数同构", "en": "algebra isomorphism", "superfield": "数学"}, {"name": "代数的中心", "en": "center of an algebra", "superfield": "数学"}, {"name": "代数的分裂域", "en": "splitting fields of algebras", "superfield": "数学"}, {"name": "代数的分裂扩张", "en": "split extension of algebras", "superfield": "数学"}, {"name": "代数的张量积", "en": "tensor product of algebras", "superfield": "数学"}, {"name": "代数的恒等式", "en": "identities of algebras", "superfield": "数学"}, {"name": "代数的标量扩张", "en": "scalar extension of algebras", "superfield": "数学"}, {"name": "代数的根", "en": "radical of an algebra", "superfield": "数学"}, {"name": "代数的表示", "en": "representation of algebras", "superfield": "数学"}, {"name": "代数论", "en": "theory of algebras", "superfield": "数学"}, {"name": "余乘法", "en": "comultiplication", "superfield": "数学"}]}, {"name": "群论", "children": [{"name": "CN群", "en": "CN-group", "superfield": "数学"}, {"name": "p共轭元", "en": "p-conjugate element", "superfield": "数学"}, {"name": "p初等群", "en": "p-elementary group", "superfield": "数学"}, {"name": "p正则元", "en": "p-regular element", "superfield": "数学"}, {"name": "p进表示", "en": "p-adic representation", "superfield": "数学"}, {"name": "r重传递群", "en": "r-fold transitive group", "superfield": "数学"}, {"name": "π可解群", "en": "π-solvable group", "superfield": "数学"}, {"name": "一般线性群", "en": "general linear group", "superfield": "数学"}, {"name": "不变式", "en": "invariant", "superfield": "数学"}, {"name": "不变式的权", "en": "weight of invariant", "superfield": "数学"}, {"name": "不变量", "en": "invariant", "superfield": "数学"}, {"name": "不可分解模表示", "en": "indecomposable modular represen- tation", "superfield": "数学"}, {"name": "不可约模特征[标]", "en": "irreducible modular character", "superfield": "数学"}, {"name": "不可约特征[标]", "en": "irreducible character", "superfield": "数学"}, {"name": "不可约表示的舒尔指数", "en": "Schur index of an irreducible representation", "superfield": "数学"}, {"name": "中心同构", "en": "central isomorphism", "superfield": "数学"}, {"name": "中心积", "en": "central product", "superfield": "数学"}, {"name": "中心自同构", "en": "central automorphism", "superfield": "数学"}, {"name": "主块", "en": "principal block", "superfield": "数学"}, {"name": "乘法群", "en": "multiplicative group", "superfield": "数学"}]}, {"name": "范畴论", "children": [{"name": "Hom函子", "en": "Hom functor", "superfield": "数学"}, {"name": "R模范畴", "en": "category of R-modules", "superfield": "数学"}, {"name": "严格归纳极限", "en": "strict inductive limit", "superfield": "数学"}, {"name": "二元函子", "en": "bifunctor", "superfield": "数学"}, {"name": "伴随函子", "en": "adjoint functors", "superfield": "数学"}, {"name": "共变函子", "en": "covariant functor", "superfield": "数学"}, {"name": "内射对象", "en": "injective object", "superfield": "数学"}, {"name": "函子", "en": "functor", "superfield": "数学"}, {"name": "函子的复合", "en": "composite of functors", "superfield": "数学"}, {"name": "函子的泛元", "en": "universal element of a functor", "superfield": "数学"}, {"name": "函子范畴", "en": "category of functors", "superfield": "数学"}, {"name": "加性函子", "en": "additive functor", "superfield": "数学"}, {"name": "加性范畴", "en": "additive category", "superfield": "数学"}, {"name": "包含函子", "en": "inclusion functor", "superfield": "数学"}, {"name": "单位函子", "en": "identity functor", "superfield": "数学"}, {"name": "单位态射", "en": "identity morphism", "superfield": "数学"}, {"name": "单态射", "en": "monomorphism", "superfield": "数学"}, {"name": "反变Hom函子", "en": "contravariant Hom functor", "superfield": "数学"}, {"name": "反变函子", "en": "contravariant functor", "superfield": "数学"}, {"name": "可表示函子", "en": "representable functor", "superfield": "数学"}]}, {"name": "非结合环", "children": [{"name": "一般凯莱代数", "en": "general Cayley algebra", "superfield": "数学"}, {"name": "上中心序列", "en": "upper central series", "superfield": "数学"}, {"name": "下中心序列", "en": "lower central series", "superfield": "数学"}, {"name": "不变多项式", "en": "invariant polynomials", "superfield": "数学"}, {"name": "不可约嘉当矩阵", "en": "irreducible Cartan matrix", "superfield": "数学"}, {"name": "交错代数", "en": "alternative algebra", "superfield": "数学"}, {"name": "代数", "en": "algebras", "superfield": "数学"}, {"name": "代数的导子", "en": "derivation of an algebra", "superfield": "数学"}, {"name": "伴随李代数", "en": "adjoint Lie algebra", "superfield": "数学"}, {"name": "伴随表示", "en": "adjoint representation", "superfield": "数学"}, {"name": "例外复单李代数", "en": "exceptional complex simple Lie algebras", "superfield": "数学"}, {"name": "例外若尔当代数", "en": "exceptional Jordan algebra", "superfield": "数学"}, {"name": "典型复单李代数", "en": "classical complex simple Lie algebras", "superfield": "数学"}, {"name": "典型实单李代数", "en": "classical real simple Lie algebras", "superfield": "数学"}, {"name": "内导子", "en": "inner derivation", "superfield": "数学"}, {"name": "凯莱代数", "en": "Cayley algebra", "superfield": "数学"}, {"name": "凯莱数", "en": "Cayley number", "superfield": "数学"}, {"name": "分裂李代数", "en": "split Lie algebra", "superfield": "数学"}, {"name": "半单李代数", "en": "semi-simple Lie algebra", "superfield": "数学"}, {"name": "半单李代数的根系", "en": "root system of a semi-simple Lie algebra", "superfield": "数学"}]}]}