Since the discovery of the existence of the injective hull of an arbitrary module
independently in 1952 by Shoda and in 1953 by Eckmann and Schopf, there have been …

We introduce the notions of Baer and quasi-Baer properties in a general module theoretic
setting. A module M is called (quasi-) Baer if the right annihilator of a (two-sided) left ideal of …

We introduce the notion of 𝒦-nonsingularity of a module and show that the class of 𝒦-
nonsingular modules properly contains the classes of nonsingular modules and of polyform …

For a semi-projective retractable module MR with endomorphism ring S, we prove u. dim
MR= u. dim SS, and find necessary and sufficient conditions on M in order that S be …

Let N be a submodule of a right R-module MR, and H= End (MR). Then N is said to be
projection invariant in M, denoted by N⊴ p M, if e N⊆ N for all e= e 2∈ H. We call MR π …

A module $ M $ is said to be coretractable if there exists a nonzero homomorphism of every
nonzero factor of $ M $ into $ M $. We prove that all right (left) modules over a ring are …

A right module M over a ring R is said to be retractable if Hom R (M, N)≠ 0 for each nonzero
submodule N of M. We show that M⊗ R RG is a retractable RG-module if and only if MR is …

While the research work on quasi-Baer rings has been quite extensive in existing literature,
the study of quasi-Baer modules introduced in 2004 remains quite limited with only little …

Let RM be a nonsingular module such that B= EndR (M) is left nonsingular and has as its
maximal left quotient ring, where is the injective hull of RM. Then it is shown that there is a …

We call a module essentially retractable if HomR for all essential submodules N of M. For a
right FBN ring R, it is shown that:(i) A non-zero module is retractable (in the sense that …