Croching
发表于 2025-3-21 19:22:08
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inspiration
发表于 2025-3-21 21:49:27
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Hdl348
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抛媚眼
发表于 2025-3-22 07:35:53
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兽群
发表于 2025-3-22 11:23:35
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放弃
发表于 2025-3-22 14:32:26
Abelian Categorieson 6.17), .. inherits the following properties from .: (4) (finitely) complete; (2) (finite) products; (3) kernels or equalizers; (4) images, sums, or (finite) intersections; (5) normality with epic images; (6) additive; (7) exact; (8) abelian; (9) exact and locally small (assuming . is small). More
种子
发表于 2025-3-22 19:35:31
General Wedderburn Theoremsbecause many properties of a module are characterizable by properties of its endomorphism ring. Indeed, some modules over certain rings are determined by their endomorphism rings, which is a way of saying that the modules are isomorphic if and only if their endomorphism rings are isomorphic . rings.
不持续就爆
发表于 2025-3-22 21:14:37
Semisimple Modules and Homological Dimensionmple Artinian ring is semisimple. Finite ring products of simple Artinian rings are also semisimple. The Wedderburn-Artin theorem implies the converse: Every semisimple ring is isomorphic to a finite product of full matrix rings of various degrees over various fields. These rings are also characteri
防锈
发表于 2025-3-23 04:18:20
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interrogate
发表于 2025-3-23 07:30:16
Tensor Products and Flat Modules sets, then for each . ∈ . there is a mapping ..: . → ., defined by the formula .. (.) = . (., .) ∀ . ∈ .. Symmetrically, if . ∈ ., then ..:. → . is defined by the formula .. (.) = . (., .) ∀. ∈ .. A mapping .:.×. → . is . in case ..:.→. and ..:. → . are group homomorphisms ∀. ∈ .,. ∈ .. A . map .:.