S-Strongly Finite Type Rings

Abstract

In this paper a ring means a commutative ring with identity element and S is a multiplicatively closed subset of the studied ring whose elements are regular. Inspiring from the work of J. Arnold about strongly finite type rings and D. E. Rush , s about noetherian spectrum rings, we introduce two types of rings that are S-strongly finite type rings and S-noetherian spectrum rings. We give some characterizations of these rings and we illustrate them by many examples.

An extension of $S$--noetherian rings and modules

“…Many authors have worked on S-noetherian rings and related notions, and have shown relevant results about their structure. See for instance [1,4,7,11,12,13,14].…”

An extension of S-artinian rings and modules to a hereditary torsion theory setting

“…Many authors have worked on S-noetherian rings and related notions, and shown relevant results on its structure. See for instance [3,7,10,11,12,14].…”