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arXiv · 1701.07207

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

Zehra Bilgin·Manuel L. Reyes·Ünsal Tekir
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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.

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Zehra Bilgin, Manuel L. Reyes, Ünsal Tekir. 2017-01-25. On right $S$-Noetherian rings and $S$-Noetherian modules. https://doi.org/10.1080/00927872.2017.1332199

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