Generalized*⊕Z*Supplemented Modules and Generalized*⊕Co-finitely Supplemented Modules

Aseel A. Alatuany, Wasan Kh. Alobaidy

Abstract


Let R be a commutative ring with identity, an R-module M is called G*⊕ Z*
supplemented modules, if every sub module containing Z*(M) has generalized*
supplement in M that is a direct summand of M . and an R-module M is called
generalized*co-finitely supplemented, if every co-finite has sub module of M has a
generalized* supplement in M. and M is called ⊕ co- finitely generalized*
supplemented , if every co- finite sub module of M has G*S that is direct summand of M.


Keywords


Generalized* ⊕ Z* supplemented, ⊕co-finitely generalized* supplemented modules, generalized* co- finitely supplemented modules.

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References


. R.Wisbauer,Foundations of modules and Ring theory,Gordon and Breach, Reading,(1991).

. S.H.Mohamed and B.J.Muller, Continuous and discrete modules, London Math.Sco.LNS.147, Cambridge University Press, Now York Sydny, (1990).

. M.Harade, Non-small modules and non-cosmall modules, In Ring Theory Proceedings of the 1978 Antwerp Conference, F.Van Oystaeyened .New York: Marcel Dekker.

. Y.Wang and N.Ding,"Generalized supplemented Modules"Taiwanese

journal of Math.vol.10.no.6, pp.1589-1601, 2006.

H. Calisici and E Turkmen "Generalized ⊕ supplemented modules" Algebra and discrete Mathematics" V0l .10, no .2, pp.10-18, 2010.

. B.N.Turkmen and A.pancar, "Generalized ⊕-Radical supplemented modules" Volume 2014, Article ID 603851,4 pages.

. W.khalid and A.Amer.Generalized* supplemented modules to appear in Iraq.J.of science the university of Baghdad.

. M.Tamer kosan,Generlized semiperfact Modules Vol.5(2009)58-69.

. A.Leghwel, T.Kosan, N. and A.Harmanc, Duo modules and duo ring, Far East J.Math.(2006), 341-346.

.A.c.Ozcan,Modules with small cyclic submodules in their injective

hulls,Comm.Alg, 30(4)2002,1575-1589.

. A.C.Ozcan, some characterizations of V-modules and rings, Vietnam J.Math., 26(3)(1998),253-258.

. W.Xue, Characterizations of Semiperfact andPerfact rings, Publications Matematiques, 40(1996), 115-125.

. F.W.Anderson and K.R.Fuller; Rings and Categories of modules, Graduate Texts Mathematics, vol.13, 2nd edition, Springer- Verlag, New York (1992).


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