S-Pseudo Quasi 2-Absorbing Submodules
Keywords:
S-pseudo quasi-2-absorbing submodule; pseudo quasi-2-absorbing submodule; scalar module; multiplication module; projective module; Z-regular module.Abstract
Let R be a commutative ring with identity and let Y be a unitary left R-module. We introduce the concept of an S-pseudo quasi-2-absorbing submodule as a generalization of an endomorphism 2-absorbing submodule and as a stronger form of a pseudo quasi-2-absorbing submodule. Several examples, elementary properties, and characterizations are established. In the classes of scalar and multiplication modules, the notions of S-pseudo quasi-2-absorbing and pseudo quasi-2-absorbing submodules coincide. We also give conditions under which the notions of S-pseudo quasi-2-absorbing and endomorphism 2-absorbing submodules are equivalent.
References
[1] M. A. Innam and A. H. Abdulrahman, Semi-2-absorbing submodules and semi-2-absorbing modules, International Journal of Advanced Scientific and Technical Research 5(3) (2015), 521–530. No DOI assigned by the publisher.
[2] H. K. Mohammadali and O. A. Abdalla, Pseudo 2-absorbing and pseudo semi-2-absorbing submodules, AIP Conference Proceedings 2096 (2019), 020006, 1–9. doi: 10.1063/1.5097803.
[3] A. Sh. Ajeel and H. K. Mohammadali, A note on almost approximaitly nearly prime submodules, AIP Conference Proceedings 2834 (2023), 080042. doi: 10.1063/5.0161493.
[4] O. A. Abdullah and H. K. Mohammadali, On extend nearly pseudo 2-absorbing submodules, AIP Conference Proceedings 2834 (2023), 080046. doi: 10.1063/5.0161441.
[5] O. A. Abdulla and H. K. Mohammad Ali, Pseudo quasi-2-absorbing submodules and some related concepts, Ibn Al-Haitham Journal for Pure and Applied Sciences 32(2) (2019), 114–122. doi: 10.30526/32.2.2149.
[6] K. R. Goodearl, Ring Theory: Nonsingular Rings and Modules, Marcel Dekker, New York and Basel, 1976.
[7] F. Kasch, Modules and Rings, London Mathematical Society Monographs, Academic Press, New York, 1982.
[8] D. S. Dummit and R. M. Foote, Abstract Algebra, 3rd ed., John Wiley & Sons, 2004.
[9] P. F. Smith, Some remarks on multiplication modules, Archiv der Mathematik 50 (1988), 223–235. doi: 10.1007/BF01187738.
[10] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, 2nd ed., Springer-Verlag, New York, 1992.
[11] M. S. Abbas, On Fully Stable Modules, Ph.D. thesis, University of Baghdad, Iraq, 1990.
[12] D. J. Fieldhouse, The Jacobson radical and regular modules, Canadian Mathematical Bulletin 18(1) (1975), 141–142. doi:10.4153/CMB-1975-026-5.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.
