Author:
Geroldinger Alfred,Zhong Qinghai
Abstract
AbstractThis is a survey on factorization theory. We discuss finitely generated monoids (including affine monoids), primary monoids (including numerical monoids), power sets with set addition, Krull monoids and their various generalizations, and the multiplicative monoids of domains (including Krull domains, rings of integer-valued polynomials, orders in algebraic number fields) and of their ideals. We offer examples for all these classes of monoids and discuss their main arithmetical finiteness properties. These describe the structure of their sets of lengths, of the unions of sets of lengths, and their catenary degrees. We also provide examples where these finiteness properties do not hold.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference95 articles.
1. Anderson, D.D. (ed.): Factorization in Integral Domains. Lecture Notes in Pure and Applied Mathematics, vol. 189. Marcel Dekker, New York (1997)
2. Anderson, D.D., Al-Mallah, O.A.: Commutative group rings that are présimplifiable or domainlike. J. Algebra Appl. 16, 9 (2017)
3. Anderson, D.D., Anderson, D.F., Zafrullah, M.: Factorization in integral domains. J. Pure Appl. Algebra 69, 1–19 (1990)
4. Anderson, D.D., Anderson, D.F., Zafrullah, M.: Atomic domains in which almost all atoms are prime. Commun. Algebra 20, 1447–1462 (1992)
5. Anderson, D.D.: Irreducible elements in commutative rings with zero-divisors. Houst. J. Math. 37, 741–744 (2011)
Cited by
42 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献