Let R be a commutative ring with identity. For an R-module M, the notion of α-absorbing
submodules and weakly α-absorbing submodules are defined. We study some basic …

ON β-PRIME SUBMODULES Page 1 J. Indones. Math. Soc. Vol. 25, No. 02 (2019), pp. 128–
138. ON β-PRIME SUBMODULES Thawatchai Khumprapussorn Department of Mathematics …

Let R be a commutative ring with 1 ≠ 0 1≠ 0 and M be a nonzero unital R-module. Recall
that a proper submodule N of M is called a semiprimary submodule of M if whenever rm ∈ N …

Let R be a commutative ring with identity and let M be a unitary R-module. In this paper, we
introduce the notion of weakly S-2-absorbing submodule. Suppose that S is a …

Let M be a right R-module. A right R-module N is called small principally M-injective (briefly,
SP-M-injective) if, every R-homomorphism from a small and principal submodule of M to N …

A submodule Ϝ of an R-module Ε is called small in Ε if whenever, for some submodule W of
Ε, implies. In this paper, we introduce the notion of Ζ-small submodule, where a proper …

This article introduces the concept of S‐semiprime submodules which are a generalization
of semiprime submodules and S‐prime submodules. Let M be a nonzero unital R‐module …

Let R be an associative ring with identity and let M be a unitary left R–module. As a
generalization of small submodule, we introduce Jacobson–small submodule (briefly J …

Let R be an arbitrary ring, M a rightR-module and S= EndR (M), the endomorphism ring of M.
A proper fully invariant submodule X of M is called a prime submodule of M if for any ideal I …