Nearly 2-Absorbing Submodules And Related Concepts
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Abstract
Throughout this note R is commutative ring with identity, and X be a
left unitary R-module. A proper submodule K of an R-module X is called
nearly prime, if whenever implies that either
( ) or [ ( ) ]. This concept us to introduce the
concept of nearly prime submodule, where a proper submodule K of an
R-module X is called nearly 2-absorbing submodule, if wherever
, and then either ( ) or
( ) or [ ( ) ]. The aim of this paper is to study this
concept, and gives some of its basic properties, characterization and
examples. Furthermore, we study the relation of this concept with some
kind of submodules".
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References
[1] AL-Mothafar N.S. and Abdul-Alkalik A. J. (2015). Nearly Prime Submodules. International Journal of Advanse Scientific and Technical Research, 6(5): 166-173.
[2] LU C. P. (1984). Prime Submodules of Modules. Communication Mathematics Journal, 33 : 61-69.
[3] Darani, A. Y., & Soheilnia, F. (2012). 2-absorbing and weakly 2-absorbing submodules. Thai Journal of Mathematics, 9(3): 577-584.
[4] Larsen M. D. and Mccarthy P.G. (1971). Multiplication Theory of Ideals. Acadimic Press New Yourk and London.
[5] Abdulrahman A. H. (2015). 2-Absorbing Modules and Semi 2-Absorbing Modules. M.SC. University of Baghdad.
[6] Kasch, F. (1982). Modules and rings . Academic Press.
[7] Hashem M.B. (2016). Nearly Semi - Prime Submodules. M.SC, University of Baghdad.