Commutative ring extensions defined by perfect-like conditions - Alaoui Ismaili, K.; Mahdou, N.; Moutui, M. A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 512.5 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 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 R=R/Rad(R) is semisimple and n-potents lift modulo 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.