On transfer homomorphisms in commutative rings with zero-divisors

2025/02/13 by Aqsa Bashir, Bashir, Aqsa, Mara Pompili +1 · 3 citations
Mathematics · #13A15 #13F05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2502.09418

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the arithmetic of monoids of regular elements of commutative rings with zero-divisors. Our focus is on Krull rings and on some of their generalizations (such as weakly Krull rings and C-rings). We establish sufficient conditions for a subring R of a Krull ring D guaranteeing that the inclusion R^\bullet \hookrightarrow D^\bullet of the respective monoids of regular elements is a transfer homomorphism. The arithmetic of the Krull monoid D^\bullet is well studied and the existence of a transfer homomorphism implies that R^\bullet and D^\bullet share many arithmetic properties.

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