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 equal to n. Later, Jhilal and Mahdou defined a commutative unital ring R to be strongly n-perfect if any R-module of flat dimension less than or equal to n has a projective dimension less than or equal to n. Recently, Purkait defined a ring R to be n-semiperfect if \(\overline{R }\) = R/Rad(R) is semisimple and n-potents lift modulo Rad(R). We study three classes of rings, namely, n-perfect, strongly n-perfect, and n-semiperfect rings. These notions are investigated in several ring-theoretic structures with an aim to construct new original families of examples satisfying the indicated properties and subject to various ring-theoretic properties.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 3, pp. 319–327, March, 2023. Ukrainian https://doi.org/10.37863/umzh.v75i3.6878.
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Ismaili, K.A., Mahdou, N. & Moutui, M.A.S. Commutative Ring Extensions Defined by Perfect-Like Conditions. Ukr Math J 75, 364–375 (2023). https://doi.org/10.1007/s11253-023-02204-8
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DOI: https://doi.org/10.1007/s11253-023-02204-8