On right $S$-Noetherian rings and $S$-Noetherian modules
Rings and Algebras
2017-08-15 v4 Commutative Algebra
Abstract
In this paper we study right -Noetherian rings and modules, extending of notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right -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 -Noetherian modules with the following consequence in commutative algebra: If a module over a commutative ring is -Noetherian with respect to a multiplicative set that contains no zero-divisors for , then has an associated prime.
Cite
@article{arxiv.1701.07207,
title = {On right $S$-Noetherian rings and $S$-Noetherian modules},
author = {Zehra Bilgin and Manuel L. Reyes and Ünsal Tekir},
journal= {arXiv preprint arXiv:1701.07207},
year = {2017}
}
Comments
8 pages; corrections made to Example 1 and Theorem 2.3