Generalization of Certain Characteristics of Multiplication Modules to Locally Multiplication Modules

Judi Shaho Hussein; Adil Kadir Jabbar; Hardi Nasraddin Aziz

doi:10.29196/jubpas.v34i1.6399

Article Details

Generalization of Certain Characteristics of Multiplication Modules to Locally Multiplication Modules

Authors:

Judi Shaho Hussein | Adil Kadir Jabbar | Hardi Nasraddin Aziz

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.34 Issue 1, pp.319-334

Document Type:

Article

Publication Date:

3/2026

Document Language:

English

Document ID (Org No.):

2001383434

pISSN:

2312-8135

DOI:

10.29196/jubpas.v34i1.6399

Keywords:

Abstract:

 Background: Consider a commutative ring with a non-zero identity and an module . A multiplication module is an module that satisfies the multiplication property. That is, every submodule is presented as the product of an ideal of the ring and the module itself.
Materials and Methods: An module is a locally multiplication module if or is a multiplication module for each prime ideal of . In this paper, certain properties of multiplication modules are extended to locally multiplication modules by providing conditions under which this generalization is possible.
Results: A locally multiplication module is Noetherian whenever the ring is both semi-local and satisfies the conditions of an ascending chain on ideals with prime/semiprime property. As well as, if is a faithful locally multiplication module and is a prime ideal with , then a bijection exists between ideals and submodules of and . Also, if is a locally multiplication module and as the submodule of is both prime and primary whenever the set of contained in , along with several other results. 
Conclusion: Various conditions are presented in terms of faithfulness, cyclic, prime, semi-prime, primary, and others, to illustrate the generalization of certain properties of multiplication modules to locally multiplication modules.

Article Details

Generalization of Certain Characteristics of Multiplication Modules to Locally Multiplication Modules

Authors:

Judi Shaho Hussein | Adil Kadir Jabbar | Hardi Nasraddin Aziz

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.34 Issue 1, pp.319-334

Document Type:

Article

Publication Date:

3/2026

Document Language:

English

Document ID (Org No.):

2001383434

pISSN:

2312-8135

DOI:

10.29196/jubpas.v34i1.6399

Multiplication module

faithful module

locally multiplication module

Noetherian module

prime submodule

primary submodule

semiprime submodule

Issues

Article Details

Authors: Judi Shaho Hussein | Adil Kadir Jabbar | Hardi Nasraddin Aziz

Publisher: University of Babylon

Journal: JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.34 Issue 1, pp.319-334

Document Type: Article

Publication Date: 3/2026

Document Language: English

Document ID (Org No.): 2001383434

pISSN: 2312-8135

DOI: 10.29196/jubpas.v34i1.6399

Issues

Authors:

Judi Shaho Hussein | Adil Kadir Jabbar | Hardi Nasraddin Aziz

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.34 Issue 1, pp.319-334

Document Type:

Article

Publication Date:

3/2026

Document Language:

English

Document ID (Org No.):

2001383434

pISSN:

2312-8135

DOI:

10.29196/jubpas.v34i1.6399