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- Title
Two questions on domains in which locally principal ideals are invertible.
- Authors
Xing, Shiqi; Wang, Fanggui
- Abstract
An LPI domain is a domain in which every locally principal ideal is invertible. In this paper, we give a negative answer to a question of Anderson-Zafrullah. We show that if is an LPI domain and is a multiplicatively closed set, then is not necessarily an LPI domain. Concerning a question of Bazzoni, we give a characterization of finite character for a finitely stable LPI-domain. We show that if is a finitely stable LPI-domain, then every nonzero nonunit element of is contained in only finitely many maximal ideals which are in , and is of finite character if and only if each nonzero nonunit element is contained in only finitely many nonstable maximal ideals. A maximal ideal is in provided there is a finitely generated ideal such that is the only maximal ideal containing .
- Subjects
FPF rings; MODULAR arithmetic; MODULES (Algebra); ALGEBRAIC coding theory; CODING theory
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 6, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501122