On APP-Quasi prime Submodules
DOI:
https://doi.org/10.29304/jqcsm.2024.16.21558Keywords:
Prime submodules, 2-Absorbing submodules., APP-quasi prime submodules, Multiplication modules, projective modulesAbstract
Let to be a commutative ring with identity and is a unitary left -module. In this paper we introduce the concept of approximaitly-quasi prime submodules (for short APP-quasi prime submodule) as a generalizations of prime submodule and quasi prime submodule, where a proper submodule of -module is said to be an APP-quasi prime submodule of , if whenever , where and implies that either or [5]. Many new examples, characterization and basic properties of this concepts are introduce. Furthermore new characterizations of APP-quasi prime submodules in some types of modules are given.
Downloads
References
Dauns, J., “Prime Modules,” Journal reine Angew, Math. Vol. 2, (1978), pp.156-181.
Lu, C. P., “M-radical of Submodules in Modules,” Math. Japan, Vol. 34, (1989), pp. 211-219.
Athab, E. A., “Prime and Semi-Prime,” Ph.D. Thesis; College of Scicence, University of Baghdad (1996). [4] Abdul-Razak H.M., “Quasi-Prime Modules and Quasi-Prime subModules,” M.Sc. Thesis, University of Baghdad (1999).
Ali Sh. And Haibat K., “Approximaitly Quasi-prime SubModules and Some Related concepts,” Journal of Al-Qadisiyah for computer science and mathematics. Vol. 11, No.(2), (2019), PP. 54-62.
Goodearl, K. R., “Ring Theory,” Marcel Dekker, Inc. New York and Basel, (1976), p. 206.
Kasch, F., “Modules and Rings,” London Math. Soc. Monographs, New York, Academic press (1982).
El-Bast, Z. A. and Smith, P. F., “Multiplication Modules,” Comm. In Algebra, Vol. 16, No.(4), (1988), pp. 755-779.
Smith, P.F.; Some Remarks On Multiplication Module; Arch. Math. Vol. 50, (1988), pp. 223-225.
Darani ,A.Y. and Soheilniai ,F″2-Absorbing and Weakly 2-Absorbing Submodules,″ Tahi Journal Math .Vol. 9, (2011), pp.577-584.
Zelmanowitz, J., “Regular Modules,” Trans .Amerecan ,Math. Soc. Vol. 163, (1973) , pp. 341-355.
Nuha ,H.H ., “The Radicals of Modules,” M.Sc. Thesis ,University of Baghdad (1996),.
Naderi. M. and Reza. J., “Weakly Primary Submodules of Multiplication Modules and Intersection Theorem,” Int. Journal Contemp. Math. Sci, Vol. 4, No.(33), (2009), PP. 1645 -1652.
Ali, S. M., ″On Concellation Modules″, M. Sc. Thesis, University of Baghdad , (1993).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Thaer Z. Khlaif, Haibat K. Mohammadali, Akram S. Mohammed
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
