On Nonnil-<i>S</i>-Noetherian Rings

Abstract

Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.

Keywords

• nonnil-S-Noetherian ring
• S-Noetherian ring
• S-finite ideal
• SFT ring