Commutative ring extensions defined by perfect-like conditions

KA Ismaili, N Mahdou, MAS Moutui - Ukrainian Mathematical Journal, 2023 - Springer
In 2005, Enochs, Jenda, and López-Romos extended the notion of perfect rings to n-perfect
rings such that a ring is n-perfect if every flat module has projective dimension less than or …

On generalizations of semiperfect and perfect rings

Y Mehmet Demirci - Bulletin of the Iranian Mathematical Society, 2016 - bims.iranjournals.ir
‎ We call a ring $ R $ right generalized semiperfect if every simple right $ R $-module is an
epimorphic image of a flat right $ R $-module with small kernel‎,‎ that is‎,‎ every simple right $ R …

Generalizations of perfect, semiperfect, and semiregular rings

Y Zhou - Algebra colloquium, 2000 - Springer
For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

Almost-perfect rings and modules

B Amini, A Amini, M Ershad - Communications in Algebra®, 2009 - Taylor & Francis
Following, a ring R is called right almost-perfect if every flat right R-module is projective
relative to R. In this article, we continue the study of these rings and will find some new …

[PDF][PDF] Amalgamated ring defined by the (n, d)-perfect property.

KA Ismaili - Palestine Journal of Mathematics, 2023 - pjm.ppu.edu
In [21], Jhilal and Mahdou defined a commutative unital ring R to be an (n, d)-perfect ring, if
every n-presented module with flat dimension at most d, has projective dimension at most d …

Characterizations of semiperfect and perfect rings

W Xue - Publicacions Matematiques, 1996 - JSTOR
We characterize semiperfect modules? semiperfect rings, and perfect rings using locally
projective covers and generalized locally projective covers, where locally projective …

On Strong n-Perfect Rings

A Jhilal, N Mahdou - Communications in Algebra®, 2010 - Taylor & Francis
In this article we introduce and investigate a particular class of n-perfect rings that we call
“strong n-perfect rings.” We are mainly concerned with this class of rings in the context of …

Characterizations of right perfect rings by⊕-supplemented modules

D Keskin - Contemporary Mathematics, 2000 - books.google.com
The aim of this note is to characterize right perfect rings using€ 9–supplemented modules.
Let R be a ring. We prove that R is a right perfect ring if and only if every T-projective right R …

Rings over which flat covers of finitely generated modules are projective

A Amini, M Ershad, H Sharif - Communications in Algebra, 2008 - Taylor & Francis
In Bican et al., it is proved that all modules over an arbitrary ring have flat covers. In this
article, we shall study rings over which flat covers of finitely generated modules are …

[PDF][PDF] On Purely–Extending Modules

B Al-Bahrani - Iraqi Journal of Science, 2013 - iasj.net
In this note we consider a generalization of the notion of a purely extending modules,
defined using y–closed submodules. We show that a ring R is purely y–extending if and only …