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  2. Volume 2, Issue 2
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Online ISSN: 2788-6867

Volume2, Issue2

Some Properties of Strongly Principally Self-Injective Modules

    Khalid S. Munshid Mohanad F. Hamid Jehad R. Kider

Journal of Applied Sciences and Nanotechnology, 2022, Volume 2, Issue 2, Pages 132-141
10.53293/jasn.2021.3248.1096

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Abstract

The idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules. A number of characteristics and characterizations of such modules have been established. In addition, the idea of strongly mainly self-pure sub-modules was added, which is similar to strongly primarily self-injective sub-modules. Some characteristics of injective, quasi-injective, principally self-injective, principally injective, absolutely self-pure, absolutely pure, and finitely R-injective modules being lengthened to strongly principally self-injective modules. So, in the present work, some properties are added to the concept in a manner similar to the absolutely self-neatness. The fundamental features of these concepts and their interrelationships are linked to the conceptions of some rings. (Von Neumann) regular, left SF-ring, and left pp-ring rings are described via such concept. For instance, the homomorphic picture of every principally injective module be strongly principally self-injective if R being left pp-ring, and another example for a commutative ring R of every strongly principally self-injective module be flat if R being (Von Neumann) regular. Also, a ring R be (Von Neumann) regular if and only if each R-module being strongly principally self-injective module.
Keywords:
    Absolutely self-pure Principally self-injective Quasi injective Strongly principally self-injective
Main Subjects:
  • Applied Mathematics
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(2022). Some Properties of Strongly Principally Self-Injective Modules. Journal of Applied Sciences and Nanotechnology, 2(2), 132-141. doi: 10.53293/jasn.2021.3248.1096
Khalid S. Munshid; Mohanad F. Hamid; Jehad R. Kider. "Some Properties of Strongly Principally Self-Injective Modules". Journal of Applied Sciences and Nanotechnology, 2, 2, 2022, 132-141. doi: 10.53293/jasn.2021.3248.1096
(2022). 'Some Properties of Strongly Principally Self-Injective Modules', Journal of Applied Sciences and Nanotechnology, 2(2), pp. 132-141. doi: 10.53293/jasn.2021.3248.1096
Some Properties of Strongly Principally Self-Injective Modules. Journal of Applied Sciences and Nanotechnology, 2022; 2(2): 132-141. doi: 10.53293/jasn.2021.3248.1096
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Journal Information

Publisher: University of Technology - IRAQ

Email:  jasn@uotechnology.edu.iq

Editor-in-chief: Prof. Dr. Adawiya J. Haider

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Applied Sciences and Nanotechnology (JASN)

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