grotto
发表于 2025-3-23 12:11:51
Morita Theorems and the Picard Group of the Picard group Pic (mod-.) of all .-linear auto-equivalences of mod-. for an arbitrary algebra ., and also (in Exercises for Chapter 12, and in Chapter 32) of the Brauer group of a commutative ring .
Transfusion
发表于 2025-3-23 17:13:58
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表否定
发表于 2025-3-23 19:39:30
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Spina-Bifida
发表于 2025-3-23 23:37:02
Synthesis Lectures on Data Managementy generated projective faithful left .-module over any ring ., and . = End.. then there is a lattice isomorphism . where . is the trace of . in . (Correspondence Theorem for Projective Modules.) This isomorphism sends (., .)-submodules of . into (ideals of .) .. Thus, when . = . (and only then) the two theorems coincide.
充足
发表于 2025-3-24 04:57:26
Logic and Relational Databases,ng functors, right continuous functors, Freyd’s theorems, module valued adjoints, the tensor functor, flat modules, character modules, adjoints of faithful functors, PopescoGabriel theorem (second version), algebras over commutative rings, semigroup rings, and group rings, free algebras, commutative and noncommutative rings of polynomials.
muscle-fibers
发表于 2025-3-24 07:43:28
Existential Rules: A Graph-Based Viewf (left) exact functors . ↷ ., the direct limit.is a (left) exact functor . ↷ .. This implies that a direct limit of a directed family of flat modules in mod-. is flat, for any ring .. A colimit of colimit preserving functors is always colimit preserving (6.22).
书法
发表于 2025-3-24 13:02:08
Correspondence Theorems for Projective Modules and the Structure of Simple Noetherian Ringsy generated projective faithful left .-module over any ring ., and . = End.. then there is a lattice isomorphism . where . is the trace of . in . (Correspondence Theorem for Projective Modules.) This isomorphism sends (., .)-submodules of . into (ideals of .) .. Thus, when . = . (and only then) the two theorems coincide.
无力更进
发表于 2025-3-24 16:30:55
Limits, Adjoints, and Algebrasng functors, right continuous functors, Freyd’s theorems, module valued adjoints, the tensor functor, flat modules, character modules, adjoints of faithful functors, PopescoGabriel theorem (second version), algebras over commutative rings, semigroup rings, and group rings, free algebras, commutative and noncommutative rings of polynomials.
CODA
发表于 2025-3-24 20:56:54
Abelian Categoriesf (left) exact functors . ↷ ., the direct limit.is a (left) exact functor . ↷ .. This implies that a direct limit of a directed family of flat modules in mod-. is flat, for any ring .. A colimit of colimit preserving functors is always colimit preserving (6.22).
细节
发表于 2025-3-25 02:02:36
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