Let I be an ideal of a ring R and let M be a left R-module. A submodule L of M is said to be δ-
small in M provided M≠L+X for any proper submodule X of M with M/X singular. An R …

On rings with one middle class of injectivity domains 1. Introduction Page 1 MATHEMATICAL
COMMUNICATIONS 109 Math. Commun. 27(2022), 109–126 On rings with one middle class …

In this paper, we investigate modules whose elements of their injectivity domains satisfy the
fixed property p. In particular, quasi-poor modules as a generalization of poor modules are …

In this paper, we consider associative rings with unit and unitary modules over these rings.
Let R be a ring and M a right unitary R-module. We denote by J (R) and J (M) the Jacobson …

In this paper, we introduce principally⊕-supplemented modules as a generalization of⊕-
supplemented modules and principally lifting modules. This class of modules is a …

Let R be a commutative ring with identity and M be a unitary R-module. Let ϕ: S (M)→ S
(M)∪{∅} be a function, where S (M) is the set of submodules of M. Suppose n≥ 2 is a …

Throughout this paper all rings are commutative with nonzero identity comma and all
modules are considered to be unitary period We wish to study properties of submod hyphen …

In this paper we reconsider a classical theorem by Bican and El Bashir, which guarantees
the existence of non-trivial relatively pure submodules in a module category over a ring with …

arXiv:1005.4168v1 [math.RA] 23 May 2010 Page 1 arXiv:1005.4168v1 [math.RA] 23 May
2010 RINGS WHOSE PROPER FACTORS ARE RIGHT PERFECT ALBERTO FACCHINI …