Mine-Prime Submodules
DOI:
https://doi.org/10.29304/jqcsm.2024.16.21534Keywords:
Prime submodules, Nearly Prime submodule, Mine- Prime submodules, Multiplication, Jacobson radical of submodulesAbstract
Let be commutative rings with identity, and all modules are (left) unitary . of an G is called prime , if for any , for , , imples that either or .As strong from of prime sub modules we introduce in that paper the concept of Mine-Prime submodules and gave same basic properties , example and characterizations of this concept. Moreover we study be haver of Mine-Prime submodules in class of of multiplication modules, furthermore we prove that by examples the residual of Mine-Prime submodules not to be Mine-Prime ideal of so we gave under sertion conditions several characterizations of Mine-Prime submodules
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References
Dauns, J., (1978), “Prime Modules”, Journal Reine Angew, Math., Vol. (2), pp. (156-181).
Athab, E. A., (1996), “Prime and SemiPrime”, M.Sc. Thesis, University of Baghdad.
Abdul-Razak, M. H., (1999), “Quasi Prime Modules and Quasi Prime Submodules”, M.Sc. Thesis, University of Baghdad.
Nuhad S. A. and Mohammed B. H., (2015), “Nearly Semiprime Submodules”, Iraqi Journal of Science, Vol.(56), No. (4B), pp. (3210-3214).
Nuhad, S. A. and Adwia, J. A., (2015), “Nearly Prime Submodules”, International Journal of Advanced Scientific and Technical Research. Vol. (6), No. (5), pp. (166-173).
Nuhad, S. A. and Adwia, J. A., (2017), “Nearly Quasi Prime Submodules”, International Journal of Advanced Research, Vol. (5), No. (1), pp. (170-180).
Khadem, K. O., & Ali, H. K. M. (2022). Restrict Nearly Semiprime Submodule. Journal of University of Babylon for Pure and Applied Sciences, (165-173).
Mohammadali, H. K., & Khadem, K. O. (2023, September). Some results on restrict nearly prime submodule. In AIP Conference Proceedings (Vol. 2845, No. 1). AIP Publishing.
Burton, D. M., (1970), “A First Course in Rings and Ideals”, University of New Hampshire.
Lu, C. P., (1984), “Prime Submodules of Modules”, Commentarii mathematici Universitatis Sancti Pauli, Vol.(33), No.(1), pp.(61-69).
Anderson, F. W. and Fuller, K. R., (1992), “Rings and Categories of Modules”, Springer- Verlag New York.
Larsen, M. D. and McCarthy, P. J., (1971), “Multiplicative Theory of Ideals”, Academic press, New York and London.
Dung, N.V., Huynh, D.V., Smith, P.I., and Wishbauer, R., (1994), “Extending Modules”, Pitman Research Notes in Math. Series. Longman, Harlow.
Kasch, F., (1982), “Modules and Rings”, London Math. Soc. Monographs, New York, Academic Press.
Sharpe, D.W. and Vomos, P., (1972), “Injective Modules”, Cambridge University, press.
El-Bast, Z. A. and Smith, P. F., (1988), “Multiplication Modules”, Comm. In Algebra, Vol. (16), No. (4), pp. (755-779).
Ameri, R., (2003), “On the Prime Submodules of Multiplication Module”, International Journal of Mathematics and Mathematical Sci., Vol. (27), pp. (1715-1724).
Nuha, H. H., (1996), “The Radicals of Modules”, M.Sc. Theses, University of Baghdad.
Lu, C. P., (1989), “M-radical of Submodules in Modules”, Math. Japan, Vol. (34), pp. (211-219).
Smith, P.F., (1988), “Some Remarks on Multiplication Modules”, Arch. Math., Vol. (50), pp. (223-225).
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Copyright (c) 2024 Ali Sabah Sadip, Haibat Karim Mohammadali
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