TL;DR
This paper introduces (n,d)-perfect rings, generalizing S-rings, explores their properties, relationships with A(n) property, and examines their behavior in pullback rings.
Contribution
It defines (n,d)-perfect rings, studies their fundamental properties, and investigates their behavior in pullback constructions, extending the theory of S-rings.
Findings
(n,d)-perfect rings generalize S-rings.
Established basic properties of (n,d)-perfect rings.
Analyzed the relationship between A(n) property and (n,d)-perfect property.
Abstract
In this paper, we introduce the notion of "(n,d)-perfect rings" which is in some way a generalization of the notion of "S-rings". After we give some basic results of this rings and we survey the relationship between "A(n) property" and "(n,d)-perfect property". Finally, we investigate the "(n,d)-perfect property" in pullback rings.
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