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Titlebook: Algebra; Rings, Modules and C Carl Faith Book 1973 Springer-Verlag, Berlin · Heidelberg 1973 Autodesk Maya.Coproduct.Kategorie.Modul.algebr

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發(fā)表于 2025-3-21 19:22:08 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Algebra
期刊簡稱Rings, Modules and C
影響因子2023Carl Faith
視頻videohttp://file.papertrans.cn/153/152423/152423.mp4
學(xué)科分類Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Algebra; Rings, Modules and C Carl Faith Book 1973 Springer-Verlag, Berlin · Heidelberg 1973 Autodesk Maya.Coproduct.Kategorie.Modul.algebr
影響因子VI of Oregon lectures in 1962, Bass gave simplified proofs of a number of "Morita Theorems", incorporating ideas of Chase and Schanuel. One of the Morita theorems characterizes when there is an equivalence of categories mod-A R::! mod-B for two rings A and B. Morita‘s solution organizes ideas so efficiently that the classical Wedderburn-Artin theorem is a simple consequence, and moreover, a similarity class [AJ in the Brauer group Br(k) of Azumaya algebras over a commutative ring k consists of all algebras B such that the corresponding categories mod-A and mod-B consisting of k-linear morphisms are equivalent by a k-linear functor. (For fields, Br(k) consists of similarity classes of simple central algebras, and for arbitrary commutative k, this is subsumed under the Azumaya [51]1 and Auslander-Goldman [60J Brauer group. ) Numerous other instances of a wedding of ring theory and category (albeit a shot- gun wedding!) are contained in the text. Furthermore, in. my attempt to further simplify proofs, notably to eliminate the need for tensor products in Bass‘s exposition, I uncovered a vein of ideas and new theorems lying wholely within ring theory. This constitutes much of Chapter 4
Pindex Book 1973
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書目名稱Algebra影響因子(影響力)




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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
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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.
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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
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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 .:.
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