On right $S$-Noetherian rings and $S$-Noetherian modules

Abstract

In this paper we study right $S$-Noetherian rings and modules, extending of 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.

8 pages; corrections made to Example 1 and Theorem 2.3

References in corpus (1)

• A prime ideal principle for two-sided ideals

Cited by in corpus (1)

• Fully $S$-idempotent modules