Sets of lengths in maximal orders in central simple algebras.
TLDR
It is proved that in a large majority of cases there exists a transfer homomorphism to a monoid of zero-sum sequences over a ray class group of O, which implies that all the structural finiteness results for sets of lengths hold also true for R.About:
This article is published in Journal of Algebra.The article was published on 2013-09-15 and is currently open access. It has received 72 citations till now. The article focuses on the topics: Algebra homomorphism & Ring (mathematics).read more
Citations
More filters
Journal ArticleDOI
Factorization theory: from commutative to noncommutative settings
TL;DR: In this article, the authors studied the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles) in non-commutative rings.
Journal ArticleDOI
Arithmetic of seminormal weakly Krull monoids and domains
TL;DR: 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.
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.
References
More filters
Book
Algebraic Number Theory
TL;DR: In this paper, Algebraic integral integers, Riemann-Roch theory, Abstract Class Field Theory, Local Class Field theory, Global Class Field and Zeta Functions are discussed.
Book
Introduction to Cyclotomic Fields
TL;DR: In this paper, Dirichlet characters were used to construct p-adic L-functions and Bernoulli numbers, which are then used to define the class number formula.
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.