A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems

DOI10.1142/S0219498815500164zbMath1385.16003arXiv1404.7264MaRDI QIDQ5498572

David J. Grynkiewicz, Alfred Geroldinger, Nicholas R. Baeth, Daniel Smertnig

Publication date: 9 February 2015

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.7264

zbMATH Keywords

direct-sum decompositionsindecomposable moduleszero-sum sequencesKrull monoidshereditary Noetherian prime ringsPrüfer rings

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60) Noetherian rings and modules (associative rings and algebras) (16P40) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic theory of semigroups (20M13) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (13)

On the Davenport constant of a two-dimensional box \([\![ -1,1\!] \times [\![ -m,n]\!]\)] ⋮ The Davenport constant of a box ⋮ Lattices over Bass rings and graph agglomerations ⋮ Sets of Lengths ⋮ Long minimal zero-sum sequences over a finite subset of \(\mathbb{Z}\) ⋮ On Monoids and Domains Whose Monadic Submonoids Are Krull ⋮ Factorization in monoids by stratification of atoms and the Elliott problem ⋮ On strongly primary monoids, with a focus on Puiseux monoids ⋮ On strongly primary monoids and domains ⋮ A characterization of weakly Krull monoid algebras ⋮ Avoiding zero-sum subsequences of prescribed length over the integers ⋮ Minimal zero-sum sequences over \(-m, n\) ⋮ Davenport constant of a box in $\mathbb {Z}^2$

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