Factorization theory: from commutative to noncommutative settings
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In this article, the authors studied the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles) in non-commutative rings.About:
This article is published in Journal of Algebra.The article was published on 2015-11-01 and is currently open access. It has received 79 citations till now. The article focuses on the topics: Cancellative semigroup & Noncommutative geometry.read more
Citations
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Journal ArticleDOI
Power monoids: A bridge between factorization theory and arithmetic combinatorics
Yushuang Fan,Salvatore Tringali +1 more
TL;DR: In this article, the power monoid of a multiplicatively written monoid is considered and the set P fin (H ) of all non-empty finite subsets of H is made into a monoid, which is called the power Monoid of H and is non-cancellative unless H is trivial, by endowing it with the operation ( X, Y ) ↦ { x y : ( x, Y ) ∈ X × Y }.
Journal ArticleDOI
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.
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.
References
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Journal ArticleDOI
The String-to-String Correction Problem
TL;DR: An algorithm is presented which solves the string-to-string correction problem in time proportional to the product of the lengths of the two strings.
Book
Noncommutative Noetherian Rings
J. McConnell,J. Robson +1 more
TL;DR: The history of mathematics can be surveyed from many dierent perspectives, such as those that try to shed light on the history of particular theorems and on the people who created them as mentioned in this paper.
Book
Encyclopedia of Distances
Michel Deza,Elena Deza +1 more
TL;DR: This book begins with several metrics in classical geometry, then proceeds to applications of distance in fields like algebra and probability, eventually working through applied mathematics, computer science, physics and chemistry, social science, and even art and religion.