On strong n-perfect rings

TL;DR

This paper introduces the concept of strong n-perfect rings, generalizing n-perfect rings, explores their properties in pullback contexts, and examines their transfer to direct products, highlighting differences and similarities.

Contribution

It defines strong n-perfect rings, compares them with n-perfect rings, and studies their behavior under pullbacks and direct products, expanding the theoretical framework.

Findings

Strong n-perfect rings generalize n-perfect rings.

Some n-perfect rings are not strong n-perfect rings.

Transfer properties of strong n-perfect rings to direct products.

Abstract

In this paper we introduce the notion of "strong $n$-perfect rings" which is in some way a generalization of the notion of "$n$-perfect rings". We are mainly concerned with those class of rings in the context of pullbacks. Also we exhibit a class of $n$-perfect rings that are not strong $n$-perfect rings. Finally, we establish the transfer of this notion to the direct product notions.