QUASI-IQC-INJECTIVITY

Samir M. Saied

Abstract


In this work, the notion of injectivity relative to a class of IQC sub modules (namely, IQC-injectivity) has been introduced and studied, which is a generalization quasi-injective module. This notion is closed under direct summands. Several properties and characterizations have been given.We provide a characterization of  semi simple  Artinian ring ,  SI-ring and Dedekind domain in terms of IQC-injective R-module.

Keywords


Quasi -injective modules;IQC -injective R-module; Quasi- closed submodules ;fully continuous modules; divisible modules.

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References


. Kasch, F, Modules and Rings. Academic Press Inc. London (English Translation) (1982).

. Good earl, K.R, Ring Theory, Nonsingular Rings and Modules, Marcel Dekker. Inc.New York, (1976).

. N.V. Dung, D.V. Huynh, P.F. Smith and R. Wisbauer, Extending Modules, Pitman, (1996).

. S .Mohamed and Thanaa, Continuous modules ,Arabian J. for science and Engineering 2,107 – 112, (1976).

. ND. W. Sharpe, P. Vamos, Injective Modules, Cambridge University Press, Cam-bridge, (1972).

. R. E. Johnson and E. T. Wong: Quasi-injective modules and irreducible rings, J. London Math. Soc. 260-268, 39 (1961).

. Zhu Z. and Tan, Z. S., Minimal quasi-injective modules. Sci. Math. Jpn. 62, 465-469, (2005).

. M. A. Hadi and M. A. Ahmed, fully extending module, International Journal of Algebra, Vol. 7, 2013, no. 3, 101 - 114

. Samir M. Saied , fully continuous module, Journalof EducationforInternational ScientificConferenceVII-Faculty of Education -University of Wasit , 2169-2176, 2014.

. H. Q. Dinh, A note on pseudo-injective modules, comm. Algebra , 33 ,(2005),361-369.

. A. W. Goldie : Torsion-free modules and rings, J. Algebra, 268-287, 1, (1964).

. M. Harada, Note on quasi-injective modules, Osaka J. Math. 351-356, 2, (1965).

. Barnard, A, Multiplication modules, Journal of Algebra 71, 174-178, (1981).

. K. Varadarajan, Hopfian and co-Hopfian objects, publicacionsMathematiques, Vol 36 293-317, (1992).

. M. R. Vedadi and A. Haghany, Modules whose injective endomorphisms are essential, Journal of Algebra 243, 765-779,(2001).

. B. L. Osofsky, Rings all of whose finitely generated modules are injective, Pacific J. 645-650, Math. 14, (1964).

. O. E. Villamayor and G. O. Michler, On rings whose simple modules are injective, Algebra 25, 185-201,(1973).

. Chang -woo Han and Su-JeongChol, Generalizations of the quasi-injective modules, comm. Korean Math. Soc. 10, No.4, pp. 811-813, (1995).

. W. K. Nicholson, M. F. Yousif: Quasi-Frobenius Rings, Cambridge University Press, 2003.

. J. J. Rotman, An Introduction to Homological Algebra, New York: Academic Press, (2000).

. R.Y. C. Ming. On regular rings and self-injective rings, IV, Publications De l’institutMathematique, Nouvelle serie tome 45(59), pp. 65-72, (1989).


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