On Closed Dual Rickart Modules
DOI:
https://doi.org/10.31642/JoKMC/2018/040104Keywords:
c-d-Rickart Modules, d-Rickart Modules, Closed Simple Modules, Epi-retractable ModulesAbstract
The notion of dual Rickart modules has been studied lately. In this article, we continue investigate and study several properties of closed dual Rickart modules which explain by Ghawi Th.Y. as a proper generalization the idea of the dual Rickart modules and as a dual concept of closed Rickart modules. A right R-module M is called closed dual Rickart if, for each , is a closed sub module of M . For a module M, we verify that M is closed dual Rickart and closed simple if and only if M is coquasi-Dedekind and Extending . We also establish that if, and are closed simple modules such that is closed dual Rickart and is projective, then either or ". Furthermore, "we give a counter example to show that the direct sums of modules is not closed under closed dual Rickart"."We also give a necessity station for a finite direct sum of closed dual Rickart modules to be closed dual Rickart". Other results are provided in this work. Examples to illustrate some results and converses are givenDownloads
References
Dung, N.V.; Huyn, D.V.; Smith, P.F. and Wisbauer, R., Extending Modules, Pitman Research notes in math. Series, 313, Longman Scientific and Technical: Harlow, 1994.
Ghawi, Th.Y., Modules With Closed Intersection (Sum) Property, Ph.D. Thesis, University Of AL-Must- ansiriyah, Iraq, 2015.
Ghorbani, A.; Vedadi, M.R.,Epi-Retractable Modules And Some Applications, Bull. Iranian Math. Soc. 35, No.1, 2009, 155-166.
Hadi, I.M-A.; Ghawi, Th.Y., Modules With The Closed Sum Property, Int. Math. Forum, Vol.9, No.32, 2014, 1539-1551. DOI: https://doi.org/10.12988/imf.2014.48151
Hadi, I.M-A.; Ghawi, Th.Y., On Closed Rickart Modules, 2016, to appear.
Khuri, S.M., Endomorphism Rings And Lattice Isomorphisms, J. Algebra, No.59, 1979,401-408. DOI: https://doi.org/10.1016/0021-8693(79)90346-6
Lam, T.Y., Lectures On Modules And Rings, Springer-Verlag-Berlin, Heidelberg, Newyork, 1999. DOI: https://doi.org/10.1007/978-1-4612-0525-8
Lee, G.; Rizvi, S.T. and Roman, C.S.,Dual Rickart Modules, Comm. Algebra, 39, 2011, 4036-4058. DOI: https://doi.org/10.1080/00927872.2010.515639
Mohamed-Ali, E.A., On Ikeda-Nakayama Modules, Ph.D. Thesis, University Of Baghdad, Iraq, 2006.
Ozcan, A.C.; Harmanci, A. and Smith, P.F., Duo Modules, Glasgow math. J, 48, 2006,533-545. DOI: https://doi.org/10.1017/S0017089506003260
Rangaswamy, K. M., Abelian Groups With Endo- morphic Images Of Special Types, J. Algebra,6, 1967, 271–280. DOI: https://doi.org/10.1016/0021-8693(67)90082-8
Shihab, B.N., Scalar Reflexive Modules, Ph.D. Thesis, University Of Baghdad, Iraq, 2004.
Tutuncu, D.K.; Tribak, R., On Dual Baer Modules, Glasgow Math. J., 52(2), 2010, 261-269. DOI: https://doi.org/10.1017/S0017089509990334
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Tha'ar Younis Ghawi
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.
