On 1-semiregular and 2-semiregular rings

TL;DR

This paper investigates specific classes of semiregular rings characterized by the periodicity of finitely presented modules, providing new characterizations and examples of these rings.

Contribution

It introduces and characterizes [Formula: see text]-semiregular and [Formula: see text]-semiregular rings, expanding understanding of their properties and examples.

Findings

Identified classes of rings where finitely presented modules are periodic.

Provided characterizations of these rings using classical notions.

Constructed examples illustrating these classes.

Abstract

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these kinds of rings are particular cases of semiregular rings. So, we call them [Formula: see text]-semiregular and [Formula: see text]-semiregular rings, respectively. We establish characterizations of these rings in terms of various classical notions and we provide several examples of such rings.