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The notion of δ-semiregular modules is introduced in terms of δ-small submodules. It is
shown that a ring R is a δ-semiregular ring if and only if RR is a δ-semiregular module, if and …

Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

It is shown that every finitely generated projective module PR over a semiprime ring R has
the smallest FI-extending essential module extension (called the absolute FI-extending hull …

Let R be a ring with unit and N be the radical of R. An i?-module M is a minimal faithful i?-
module if M is faithful and no proper summand of M is faithful. R is left QF-3 if R has a unique …

Throughout, A represents an associative ring with identity and A-modules are unital. J, Z, Y
will denote respectively the Jacobson radical, the left singular ideal and the right singular …

Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a
class of modules which is an analogous of δ-supplemented modules defined by Kosan. The …

Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a
class of modules which is an analogous to δsupplemented modules and principally⊕ …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

Introduction. Let A be a ring possessing a unit element I and satisfying the minimum
condition on right (resp. left) ideals, A tight (resp. left) A-module M will be said to be quasi …