On a weak version of S-Noetherianity

Abstract

In this paper, we introduce a new class of ring called [Formula: see text]-[Formula: see text]-Noetherian ring, which is a weak version of [Formula: see text]-Noetherian ring property and study the transfer of this notion to various context of commutative ring extensions such as direct product, trivial ring extensions and amalgamation of rings. Furthermore, we define the concept of nonnil [Formula: see text]-[Formula: see text]-Noetherian ring property which is a generalization of the [Formula: see text]-[Formula: see text]-Noetherian domain property and establish a characterization of this notion using pullbacks.