On n-Perfect Rings and Cotorsion Dimension

TL;DR

This paper explores the concept of n-perfect rings, analyzing their homological properties, relationships with ring dimensions, and providing examples within known constructions to deepen understanding of their structure.

Contribution

It establishes connections between n-perfectness and homological dimensions, and offers new examples of n-perfect rings with specific properties.

Findings

n-perfectness relates to homological dimensions of rings

studies n-perfectness in known ring constructions

provides examples of n-perfect rings with special conditions

Abstract

A ring is called $n$-perfect ($n\geq 0$), if every flat module has projective dimension less or equal than $n$. In this paper, we show that the $n$-perfectness relate, via homological approach, some homological dimension of rings. We study $n$-perfectness in some known ring constructions. Finally, several examples of $n$-perfect rings satisfying special conditions are given.