On right S-Noetherian rings and S-Noetherian modules

Bilgin Z., Reyes M. L., TEKİR Ü.

COMMUNICATIONS IN ALGEBRA, vol.46, no.2, pp.863-869, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1080/00927872.2017.1332199
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.863-869
  • Keywords: Completely prime right ideals, Oka families of right ideals, point annihilator sets, right S-Noetherian rings, PRIME IDEAL PRINCIPLE
  • Marmara University Affiliated: Yes

Abstract

In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right S-Noetherian rings are given in terms of completely prime right ideals and point annihilator sets. We also prove an existence result for completely prime point annihilators of certain S-Noetherian modules with the following consequence in commutative algebra: If a module M over a commutative ring is S-Noetherian with respect to a multiplicative set S that contains no zero-divisors for M, then M has an associated prime.