strongly N-extending Strongly N-extending modules
strongly N-continuous , strongly N-qausi- continuous
Abstract
Relative extending modules and relative (quasi-)continuous modules were introduced and studied by Oshiro as a generalizations of extending modules and (quasi-) continuous respectively. On other hand, Oshiro, Rizvi and Permouth introduced N-extending and N-(quasi-) continuous modules depending where N and M are modules. is closed under submodules, essential extension and isomorphic image. A module M is N-extending if for each submodule A , there is a direct summand B of M such that A is essential in B. Moreover, a module M is strongly extending if every submodule is essential in a stable (equivalently, fully invariant) direct summand of M.
In this paper, we introduce and study classes of modules which are proper stronger than that of N-extending modules and N-(quasi-)continuous modules. Many characterizations and properties of these classes are given.
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References
[2] Al-Saadi, S.A: S-extending modules and related concepts, Ph. D. Thesis, Mustansiriyah Univ. 2007.
[3] Anderson F.W., and Fuller, K.R.: Rings and Categories of modules, Springer-Verlag. New York 1973.
[4] Dogruoz, S.: Extending modules relative to module classes, Ph. D. Thesis, Uinv. of Glasgow, 1997..
[5] Dung, N.V. ; Hunynh, D.V. ; P.F.Smith and Wisbauer, R.: Extending modules, Pitman Research Notes in Mathematics Series, 313(1994).
[6] Lopez-permonth, S.R.; Oshiro, K. ; Rizivi, S.T. : On the relative (quasi-) continuity of modules, Comm. Algebra 26(1998), 3497-3510.
[7] Oshrio, K. : Continuous modules and quasi-continuous modules, Osaka J.Math, 20(1983), 681-694.
[8] Ozcan, A. C. Duo Modules,Glasgow Math. J.Trust 48(2006)533-545.
[9] Simth, P.F. and Tercan, A. : Continuous and quasi-continuous modules, Houston Math. J 18(1992), 339-348.
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