Essentially Compressible Modules Relative to A Submodule
Keywords:Compressible module relative to a submodule, Retractable module relative to a submodule, Essentially Compressible module relative to a submodule, Essentially Retractable module relative to a submodule.
In this work, the new notion is defined namely essentially compressible relative to a submodule, as a new generalization of the compressible module relative to a submodule where a module is called compressible module relative to a submodule N of M if for all non-zero submodule of such that contains N, there exists a monomorphism f Hom( ). We study some basic properties of this class and many relationships between these classes and other related concepts are presented and studied.
Abbas, M. S., On fully stable Modules, Ph. D. Thesis, University of Baghdad, 1990.
Al-Aeashi S N and Al-Bakaa F. H, 2020 Retractable modules relative to a submodule and some generalizations, submitted.
Al-Aeashi S N and Al-Bakaa F. H, 2020 Compressible modules relative to a submodule and some generalizations, submitted.
Al-Aeashi SN, Shyaa FD, Hadi IMA. 2019 Essentially and weakly essentially coretractable modules. J. Phys.: Conf. Ser.; 1234, 012107. Doi:10.1088/1742-6596/1234/1/012107.
Al-Hosainy A M A and Kadhim H 2014 A Co-compressible Module International Research Journal of Scientific Findings 1(6).
Amini B, Ershad M, Sharif H. Coretractable modules. J. Aust. Math. Soc. 2009; 86(3): 289–304.
Baziar M., 2009 Semi-essentially compressible modules and strongly semiprime rings, International Journal of Algebra 3 (14) 685–692.
Clark J, Lomp C, Vanaja N, Wisbauer R. Lifting modules. Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkhäuser, Basel, Boston, Berlin, 2006.
Ecevit S. And Kosan M. T., 2009 "On Rings All Of Whose Modules are Retractable", Arch. Math. (Brno), 45(1), 71-74.
Elman, R. Lectures on Abstract Algebra, University of California, Los Angeles, U.S.A. 1999.
Ghorbani A. And Vedadi M. R., 2009 "Epi-Retractable Modules And Some Applications", Bull. Iranian Math. Soc. 35(1), 155-166.
Hadi I M, Al-aeashi S N and Shyaa FD. 2019 t-Essentially and weakly t-essentially coretractable modules.
Hadi I M and Al-aeashi S N 2018 Weakly coretrectable modules. J. Phys.: Conf. Ser. 1003 012061.
Hadi I M and Al-aeashi S N 2017 Strongly Coretrectable modules Iraqi journal of sciences 58 2C pp 1069-1075.
Kasch, Friedrich. Modules and rings. Vol. 17. Academic press, 1982.
Khuri S.M., The endomorphism ring of a nonsingular retractable module, East-West J. Math. 2(2) (2000) 161-170.
Layla S M & Israa H M. 2016 Small Compressible Modules And Small Retractable Modules. International Journal Of Applied Mathematics & Statistical Sciences, 5(2) 15-28.
Moniri A. R, Talebi Y, 2019 Coretractable modules relative to a submodule, J. Algebra Comb. Discrete Appl. 6(2): 95–103.
Wisbauer, Robert. Foundations of module and ring theory. Routledge, 2018.
How to Cite
Copyright (c) 2020 Shukur Neamah Al-Aeashi, Fatimah Hussein Al-Bakaa
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.