Let R be a ring with 1∈ R. In Mod-R the total Tot (M, N) is a semi-ideal, which contains the
radical Rad (M, N), the singular ideal△(M, N) and the cosingular ideal▽(M, N). We study …

ON RINGS WHOSE PRIME IDEALS ARE MAXIMAL -Bulletin of the Korean Mathematical
Society Article Info. 1.Home 2.Article Info. Bulletin of the Korean Mathematical Society (대한수 …

Let U be a submodule of a module M. We call U a strongly lifting submodule of M if
whenever M/U=(A+ U)/U⊕(B+ U)/U, then M= P⊕ Q such that P≤ A,(A+ U)/U=(P+ U)/U and …

At the spring meeting of the Mathematical Society of Japan, in 1968, professors K. Morita
and H. Tachikawa gave a lecture entitled “On semiprimary QF-3 rings,” in which they have …

This paper is a continuation of our previous article (Behbood and Bigdeli in Commun
Algebra 47: 3995–4008, 2019). We study commutative rings R whose proper (prime) ideals …

Abstract Let p: M→ N be a right minimal epimorphism. We prove that there exists a ring
isomorphism between two rings END RM (N)/J (END RM (N)) and END RN (M)/J (END RN …

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 …

Given a module M over a ring R, G. Azumaya [1] introduced the dual notions of M-projective
and M-injective modules. These concepts have actually led MS Shrikhande to a study of …

Let $ _RM $ be a nonsingular left $ R $-module whose Morita context is nondegenerate, let
$ B=\operatorname {End} _ {R} M $ and let ${M^*}=\operatorname {Hom} _ {R}(M, R) $. We …

In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules
as a generalization to the type of R-maximal submodule, where a proper submodule of an R …