Abelian extensions of algebras in congruence-modular varieties

2000/05/13 by William H. Rowan, Rowan, William H.
Computer Science · Mathematics · #08B99 (Secondary) #18G60 (Primary) #Advanced Algebra and Logic #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:08B99 #msc:18G60

paper · pdf · doi:10.48550/arxiv.math/0005134

30 pages

arxiv created 2000/05/13 · openalex publication_date 2000/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone cohomology, such that the cohomology group in dimension one is the group of equivalence classes of extensions.

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