Approximaitly quasi-prime submodules and some related concepts

Other Title(s)

المقاسات الجزئية الأولية الظاهرية تقريبا ومفاهيم ذات علاقة

Joint Authors

Muhammad Ali, Haybat Karim
Ujayl, Ali Shibl

Source

al-Qadisiyah Journal for Computer Science and Mathematics

Issue

Vol. 11, Issue 2 (30 Jun. 2019), pp.54-62, 9 p.

Publisher

University of al-Qadisiyah College of computer Science and Information Technology

Publication Date

2019-06-30

Country of Publication

Iraq

No. of Pages

9

Main Subjects

Mathematics

Abstract EN

“Let R be a commutative ring with identity and B is a left unitary R-module.

A proper submodule E of B is called a quasi-prime submodule, if whenever rsb∈E, where r,s∈R, b∈B implies that either rb∈E or sb∈E”.

As a generalization of a quasi-prime submodules, in this paper we introduce the concept of approximaitly quasi-prime submodules, where a proper submodule E of B is an approximaitly quasi-prime submodule, if whenever rsb∈E, where r,s∈R, b∈B implies that either rb∈E+soc(B) or sb∈E+soc(B), where soc(B) is the intersection of all essential submodules of B.

Many basic properties, characterization and examples of this concept are given.

Furthermore, we study the behavior of approximaitly quasi-prime submodules under R-homomorphisms.

Finally, we introduced characterizations of approximaitly quasi-prime submodule in class of multiplication modules.

American Psychological Association (APA)

Muhammad Ali, Haybat Karim& Ujayl, Ali Shibl. 2019. Approximaitly quasi-prime submodules and some related concepts. al-Qadisiyah Journal for Computer Science and Mathematics،Vol. 11, no. 2, pp.54-62.
https://search.emarefa.net/detail/BIM-883447

Modern Language Association (MLA)

Muhammad Ali, Haybat Karim& Ujayl, Ali Shibl. Approximaitly quasi-prime submodules and some related concepts. al-Qadisiyah Journal for Computer Science and Mathematics Vol. 11, no. 2 (2019), pp.54-62.
https://search.emarefa.net/detail/BIM-883447

American Medical Association (AMA)

Muhammad Ali, Haybat Karim& Ujayl, Ali Shibl. Approximaitly quasi-prime submodules and some related concepts. al-Qadisiyah Journal for Computer Science and Mathematics. 2019. Vol. 11, no. 2, pp.54-62.
https://search.emarefa.net/detail/BIM-883447

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references : p. 61

Record ID

BIM-883447