On Nonnil-S-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.

Graded S-Noetherian Modules

“…Thereafter S-Noetherian rings and modules were continuously studied by many authors (see [4], [6], [10], [11], [12], [13], [14], [15] and [16], for example). This notion has motivated many researchers to study S-version of known structures in ring and module theory (see [4], [6], [21] and [22], for example).…”