Ž. It is well known that pure-injective s algebraically compact modules behave well in
relation to direct sum decompositions. Any indecomposable wx pure-injective module has …

The notation in this paper will be standard and it may be found in [2] or [8]. Throughout the
paper, the notation A⊂'B will mean that A is an essential submodule of the module B. Given …

A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Characteristic submodules of injective modules over strongly prime rings Page 1 DOI
10.1515/dma-2014-0022 Discrete Math. Appl. 2014; 24 (4):253–256 Askar A. Tuganbaev …

In [3], Bass has shown that a ring R is left perfect if and only if every flat left R-module is
projective and if and only if R satisfies the descending chain condition on principal right …

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) …

The purpose of this paper is to initiate the study of improjective modules. A module X is im-
projective if given any epimorphism/: B-> A and any homomorphism/: X-> A, there exists a …

Almost Projective and Almost Injective Modules Page 1 ISSN 0001-4346, Mathematical
Notes, 2018, Vol. 103, No. 1, pp. 3–17. © Pleiades Publishing, Ltd., 2018. Original Russian …

In the special case when the ring is regular as well as Noetherian, the problem is already
solved since over such a ring every module is known to be semi-simple [9] and hence is its …