Let R be a commutative ring with identity and let M be an R-module. The purpose of this
paper is to introduce and investigate the submodules of an R-module M which satisfy the …

Let R be a commutative ring with 1≠ 0 and M a unital R-module. M is said to satisfy Property
(A) if for each finitely generated ideal J of R contained in ZR (M), there exists 0≠ m∈ M such …

Let R be a commutative ring and M an R-module. Let Z (M)={r∈ R| rm= 0 for some nonzero
m∈ M} and T (M)={m∈ M| rm= 0 for some nonzero r∈ R}. M satisfies Property A …

[2108.08237] The dual of the notions r-submodules, n-submodules, and J-submodules Skip to
main content Cornell University We gratefully acknowledge support from the Simons …

In this paper, we define nilpotent elements and nilpotent submodules of a module M over a
commutative ring R. We show that if R has the ascending chain condition, then the singular …

Let be a unitary left R-module on associative ring with identity. A submodule of is called-
annihilator small if, where is a submodule of, implies that ann ()= 0, where ann () indicates …

Let and be rings. The objective is to study the bimodule satisfying the annihilator conditions
for all. This approach will clearly show how the ring or the module is connected to the …

arXiv:2208.14840v1 [math.AC] 31 Aug 2022 Page 1 arXiv:2208.14840v1 [math.AC] 31 Aug
2022 SEMIANNIHILATOR SMALL SUBMODULES WITH RESPECT TO AN ARBITRARY …

Let be a unitary left R-module on associative ring with identity. Asubmodule of is called-
annihilator small if, where is asubmodule of, implies that ann ()= 0, where ann () indicates …

Let $ R $ be a commutative ring with identity and let $ M $ be an $ R $-module. A proper
submodule $ N $ of $ M $ is said to be an $ r $-submodule if $ am\in N $ with $(0: _Ma)= 0 …