On half-factoriality of transfer Krull monoids

DOI10.1080/00927872.2020.1800720zbMath1457.13043arXiv1911.04267OpenAlexW3048303582MaRDI QIDQ3386856

Chao Liu, Salvatore Tringali, Weidong Gao, Qinghai Zhong

Publication date: 7 January 2021

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

Full work available at URL: https://arxiv.org/abs/1911.04267

zbMATH Keywords

half-factorialsets of lengthstransfer Krull monoids

Mathematics Subject Classification ID

Commutative semigroups (20M14) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (4)

On transfer Krull monoids ⋮ Length-factoriality in commutative monoids and integral domains ⋮ Arithmetic of additively reduced monoid semidomains ⋮ On the arithmetic of stable domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A quasi-local half-factorial domain with an atomic non-half-factorial integral closure
• Factorization theory: from commutative to noncommutative settings.
• Arithmetic of seminormal weakly Krull monoids and domains
• Half-factorial subrings of factorial domains
• Power series extensions of half-factorial domains
• Arithmetical characterization of class groups of the form \(\mathbb Z/n\mathbb Z\oplus\mathbb Z/n\mathbb Z\) via the system of sets of lengths.
• Bifurcus semigroups and rings.
• Monoids determined by a homogeneous linear Diophantine equation and the half-factorial property
• Geometric notes on monoids
• Power monoids: a bridge between factorization theory and arithmetic combinatorics
• On large half-factorial sets in elementary \(p\)-groups: maximal cardinality and structural char\-ac\-ter\-i\-zation.
• Half-factorial-domains
• Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid
• Factorization theory in commutative monoids
• Differences in sets of lengths of Krull monoids with finite class group.
• Sets of lengths in maximal orders in central simple algebras.
• On the maximal cardinality of half-factorial sets in cyclic groups
• The set of minimal distances in Krull monoids
• A NEW CHARACTERIZATION OF HALF-FACTORIAL KRULL MONOIDS
• On c-semigroups
• Half factorial domains
• Factorizations of distinct lengths in algebraic number fields
• Sets of Lengths
• Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules
• Factorizations in Bounded Hereditary Noetherian Prime Rings
• The monotone catenary degree of monoids of ideals
• A Characterization of Algebraic Number Fields with Class Number Two

This page was built for publication: On half-factoriality of transfer Krull monoids