Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules

DOI10.1142/S0219498817502346zbMath1441.20041arXiv1612.03116OpenAlexW3103884926MaRDI QIDQ4594963

Yushuang Fan, Florian Kainrath, Salvatore Tringali, Alfred Geroldinger

Publication date: 27 November 2017

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

Full work available at URL: https://arxiv.org/abs/1612.03116

zbMATH Keywords

factorizationsdirect-sum decompositionKrull monoidssets of lengths

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Commutative semigroups (20M14) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic theory of semigroups (20M13)

Related Items (27)

Semigroups of non-negative integer-valued matrices ⋮ An abstract factorization theorem and some applications ⋮ Lattices over Bass rings and graph agglomerations ⋮ Power monoids: a bridge between factorization theory and arithmetic combinatorics ⋮ Upper triangular matrices over information algebras ⋮ A characterization of finite abelian groups via sets of lengths in transfer Krull monoids ⋮ Monoids of sequences over finite abelian groups defined via zero-sums with respect to a given set of weights and applications to factorizations of norms of algebraic integers ⋮ Unnamed Item ⋮ Factorization under local finiteness conditions ⋮ ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS ⋮ On product-one sequences over subsets of groups ⋮ On Monoids of Ideals of Orders in Quadratic Number Fields ⋮ Commutative rings with absorbing factorization ⋮ On strongly primary monoids, with a focus on Puiseux monoids ⋮ The monotone catenary degree of monoids of ideals ⋮ On strongly primary monoids and domains ⋮ Sets of lengths in atomic unit-cancellative finitely presented monoids ⋮ On finite molecularization domains ⋮ On the arithmetic of stable domains ⋮ Structural properties of subadditive families with applications to factorization theory ⋮ Factorization theory in commutative monoids ⋮ Factorization invariants of Puiseux monoids generated by geometric sequences ⋮ On half-factoriality of transfer Krull monoids ⋮ On \(n\)-absorbing ideals of locally divided commutative rings ⋮ Unnamed Item ⋮ A characterization of length-factorial Krull monoids ⋮ Associates, irreducibility, and factorization length in monoid rings with zero divisors

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