TY - JOUR
AU - K. Alaoui Ismaili
AU - N. Mahdou
AU - M. A. S. Moutui
PY - 2023/04/11
Y2 - 2024/03/05
TI - Commutative ring extensions defined by perfect-like conditions
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 75
IS - 3
SE - Research articles
DO - 10.37863/umzh.v75i3.6878
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6878
AB - UDC 512.5In 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 or equal than $n$. Later, Jhilal and Mahdou defined a commutative unital ring $R$ to be strongly $n$-perfect if any $R$-module of flat dimension less or equal than $n$ has a projective dimension less or equal than $n$. Recently Purkait defined a ring $R$ to be $n$-semiperfect if $\overline{R}=R/{\rm Rad}(R)$ is semisimple and $n$-potents lift modulo ${\rm Rad}(R).$ We study of three classes of rings, namely, $n$-perfect, strongly $n$-perfect, and $n$-semiperfect rings. We investigate these notions in several ring-theoretic structures with an aim of construction of new original families of examples satisfying the indicated properties and subject to various ring-theoretic properties.
ER -