An abstract factorization theorem and some applications

DOI10.1016/j.jalgebra.2022.03.023zbMath1495.13004arXiv2102.01598OpenAlexW4220687101WikidataQ115193758 ScholiaQ115193758MaRDI QIDQ2132471

Salvatore Tringali

Publication date: 28 April 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.01598

zbMATH Keywords

ordersfactorizationatomschain conditionspreordersNoetherianirreduciblesACCDCCArtinianquasi-orderspower monoids

Mathematics Subject Classification ID

Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Ordered semigroups and monoids (06F05) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13)

Related Items (3)

Factorization under local finiteness conditions ⋮ A characterisation of atomicity ⋮ Apéry sets and the ideal class monoid of a numerical semigroup

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monoids of modules and arithmetic of direct-sum decompositions.
• Factorization theory: from commutative to noncommutative settings.
• The ascending chain condition for principal left or right ideals of skew generalized power series rings.
• What's so special about Kruskal's theorem and the ordinal \(\Gamma{}_ 0\)? A survey of some results in proof theory
• Power monoids: a bridge between factorization theory and arithmetic combinatorics
• Products of elementary matrices and non-Euclidean principal ideal domains
• Factorization in commutative rings with zero divisors
• Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
• On the arithmetic of power monoids and sumsets in cyclic groups
• Lattices over Bass rings and graph agglomerations
• Factorization theory in commutative monoids
• Free ideal rings
• On the structure of semigroups
• Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules
• Permutations as Products of Transpositions
• Factorization Theory and Decompositions of Modules
• Semilocal Categories and Modules with Semilocal Endomorphism Rings
• The monotone catenary degree of monoids of ideals
• Torsion Modules Over Free Ideal Rings
• On products of idempotent matrices

This page was built for publication: An abstract factorization theorem and some applications