Commutative ring extensions defined by perfect-like conditions

  • K. Alaoui Ismaili Laboratory of Mathematics, Computing and Applications-Information Security (LabMia-SI), Department of Mathematics, Faculty of Sciences of Rabat, Mohammed V University in Rabat, Morocco
  • N. Mahdou Department of Mathematics, Faculty of Science and Technology of Fez, University S. M. Ben Abdellah Fez, Morocco
  • M. A. S. Moutui University of Haute Alsace, IRIMAS, De ́partement de Mathe ́matiques, Mulhouse, France and Division of Science, Technology and Mathematics, American University of Afghanistan, Doha Campus, Qatar
Keywords: perfect, n-perfect, strongly n-perfect, (n, d)-ring, nsemiperfect, Von Neumann Regular ring, amalgamated algebra, amalgamated duplication.


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 $\overline{R}=R/{\rm Rad}(R)$ 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.


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How to Cite
Alaoui Ismaili, K., N. Mahdou, and M. A. S. Moutui. “Commutative Ring Extensions Defined by Perfect-Like Conditions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 3, Apr. 2023, pp. 319-27, doi:10.37863/umzh.v75i3.6878.
Research articles