publication . Article . 2004

AP-domains and unique factorization

Coykendall, Jim; Zafrullah, Muhammad;
Open Access
  • Published: 01 May 2004 Journal: Journal of Pure and Applied Algebra, volume 189, pages 27-35 (issn: 0022-4049, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Abstract In this paper we generalize the standard notion of unique factorization domains to the nonatomic situation. The main result of this paper is that, in contrast to the atomic situation, the assumption that every irreducible is prime (atoms prime) and the notion that every (atomic) nonzero nonunit can be factored uniquely into irreducible elements are distinct notions.
Subjects
arXiv: Physics::Atomic Physics
free text keywords: Algebra and Number Theory, Irreducible element, Prime element, Topology, Mathematics, Prime (order theory), Unique factorization domain, Algebra
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