Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition,
where a module M is called a C3-module if whenever A and B are direct summands of M …

In this paper, δ-lifting and δ-supplemented modules are defined as generalizations of lifting
and supplemented modules. Several properties of these modules are proved. New …

If I is an ideal of a ring R, we say that idempotents lift strongly modulo I if, whenever a2− a∈
I, there exists e2= e∈ aR (equivalently e2= e∈ Ra) such that e− a∈ I. The higher socles of …

If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-
homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple …

Following (Kosa̧n in Algebra Colloq. 14: 53–60, 2007), a module M is called δ-
supplemented if, for every submodule of N of M, there exists L≤ N such that M= N+ L and …

In this paper, the structure of e-local modules and classes of modules via essentially small
are investigated. We show that the following conditions are equivalent for a module M:(1) M …

Motivated by a result of Mochizuki [Mochizuki, H.(1965). Finitistic global dimension for rings.
Pacific J. Math. 15 (1): 249–258] that, for a left perfect ring R with Jacobson radical if and …

g-Coatomic Modules Page 1 Volume 2 Issue 2 Article 9 g-Coatomic Modules Ahmed H. Alwan
Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar …

Let M be a left R-module and F a submodule of M for any ring R. We call MF-semiregular if
for every x∈ M, there exists a decomposition M= A⊕ B such that A is projective, A≤ Rx and …