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Strongly nearly-2-absorbing submodules

Let Ɍ be a commutative ring with identity and V be a unitary left Ɍ-module. The concept of Strongly Nearly-2-Absorabing sub-modules as a generalization of Endo-2-Absorabing sub-modules and strong form of Nearly-2-Absorabing sub-modules are introduced in this paper. Many examples, basic properties of this concept are introduced. Furthermore we prove that in class of (scalar, cyclic and finitely-generated) modules the two concepts Nearly-2-Absorabing sub-modules and Strongly Nearly-2-Absorabing sub-modules are equivalent. Moreover we prove that Endo-2-Absorabing and Strongly Nearly-2-Absorabing sub-modules are equivalent in class of (semi simple, regular) modules. Also those concepts are equivalent in class of all modules over a v-ring. Finally we prove several characterizations of Strongly Nearly-2-Absorabing sub-modules in some types of modules such as (projective, faithful and content) modules in class of cyclic modules.

EDP Sciences

Shwkaea M. Rajab Haibat K. Mohammadali

BIO Web of Conferences

2024

Title: Strongly nearly-2-absorbing submodules

Description:

Let Ɍ be a commutative ring with identity and V be a unitary left Ɍ-module.

The concept of Strongly Nearly-2-Absorabing sub-modules as a generalization of Endo-2-Absorabing sub-modules and strong form of Nearly-2-Absorabing sub-modules are introduced in this paper.

Many examples, basic properties of this concept are introduced.

Furthermore we prove that in class of (scalar, cyclic and finitely-generated) modules the two concepts Nearly-2-Absorabing sub-modules and Strongly Nearly-2-Absorabing sub-modules are equivalent.

Moreover we prove that Endo-2-Absorabing and Strongly Nearly-2-Absorabing sub-modules are equivalent in class of (semi simple, regular) modules.

Also those concepts are equivalent in class of all modules over a v-ring.

Finally we prove several characterizations of Strongly Nearly-2-Absorabing sub-modules in some types of modules such as (projective, faithful and content) modules in class of cyclic modules.

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Strongly nearly-2-absorbing submodules

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