Arithmetic of seminormal weakly Krull monoids and domains
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In this article, the arithmetic of weakly Krull monoids with finite class group and prime divisors was studied, and it was shown that unions of sets of lengths are intervals and a characterization of halffactoriality was given.About:
This article is published in Journal of Algebra.The article was published on 2015-12-15 and is currently open access. It has received 56 citations till now. The article focuses on the topics: Group (mathematics) & Arithmetic function.read more
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Factorization theory in commutative monoids
Alfred Geroldinger,Qinghai Zhong +1 more
TL;DR: A survey on factorization theory can be found in this article, where finitely generated monoids (including affine monoids), primary monoids, power sets with set addition, Krull monoids and their various generalizations, and multiplicative monoids of domains (including Krull domains, rings of integer-valued polynomials, orders in algebraic number fields) are discussed.
Journal ArticleDOI
Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules
TL;DR: In this article, the Structure Theorem for Unions is verified for a variety of possibly non-cancellative semigroups, including semigroup of (not necessarily invertible) ideals and semiigroups of modules.
Posted Content
Sets of Lengths
TL;DR: In this paper, the authors provide a friendly introduction to what is known about systems of sets of lengths for rings of integers of algebraic number fields and for transfer Krull monoids of finite type as their generalization.
Book ChapterDOI
Systems of sets of lengths: transfer krull monoids versus weakly krull monoids
TL;DR: In this article, the Structure Theorem for Sets of Lengths of Transfer Krull Monoids (TKM) was shown to be equivalent to the structure theorem for sets of lengths of weakly-Krull monoids.
Journal ArticleDOI
On strongly primary monoids, with a focus on Puiseux monoids
TL;DR: In this paper, the authors studied the tameness of strongly primary Puiseux monoids and established an algebraic characterization of globally tame tameness, and obtained a result on the structure of sets of lengths of locally tame strongly primary monoids.
References
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Journal ArticleDOI
I and i
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Book
Cohen-Macaulay rings
Winfried Bruns,H. Jürgen Herzog +1 more
TL;DR: In this article, the authors present a self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules.
Reference BookDOI
Non-Unique Factorizations : Algebraic, Combinatorial and Analytic Theory
TL;DR: In this article, an abstract structure theorem for Sets of Lengths of Powers of an Element has been proposed for finite Abelian groups, which is based on the Dirichlet series.