Strongly Weakly Supplement Extending Modules
Keywords:Keywords, extending module, strongly extending module, weakly supplement submodule, weakly supplement extending module, strongly weakly supplement extending module.
In this paper, a class of modules which are proper strong concept of weakly supplement extending modules will be introduced and studied. We call a module M is strongly weakly supplement extending, if each submodule of M is essential in fully invariant weakly supplement submodule in M. Many characterizations of strongly weakly supplement extending modules are obtained. We show that M is strongly weakly supplement extending module if and only if every closed submodule of M is fully invariant weakly supplement submodule in M. Also we study the relation among this concept and other known concepts of modules. Moreover, we give some conditions that of strongly weakly supplement extending modules is closed under direct sum property is strongly weakly supplement extending.
M. S. Abbas: On fully stable modules, Ph. D. Thesis, Univ. of Baghdad 1991.
A. A. Ahmed: On submodules of multiplication modules, M. Sc. Thesis, Univ. of Baghdad 1992.
S. A. Al-Saadi,: S-Extending modules and related concepts, Ph. D. Thesis, Univ. of Mustansiriyah, 2007.
A. A. Al-Rubaye; S. A. Al-Saadi,: Weakly supplement extending modules, To appear. Baghdad Science Journal.
S. E. Atani; M. Khoramdel and S. D. P. Hesari: On strongly extending modules, Kyungpook Math. J. 54, 237-247, 2014. [CrossRef]
N. V. Dung; D. V. Huynh; P. F. Smith; R. Wisbauer: Extending modules, Pitman Research Notes in Math. Series, 1994.
A. Harmanci; D. Keskin; P. F. Smith: On -supplemented modules, Acta Math. Hung. 83 (1-2), 161-169, 1999. [CrossRef]
D. Keskin: On lifting modules, Comm. Algebra 28(7) 2000, 3427-3440. [CrossRef]
A. C. Ozcan; A. Harmanci; Smith, P. F.: Duo modules, Glasgow Math. J. Trust 48(2006) 533-545. [CrossRef]
R. Wisbauer: Foundations of modules and rings theory, reading, Gordon and Breach, 1991.
S. M. Yaseen: Supplement- Duo modules, J. of Progressive Research in Math. 2017.
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