Generalization of Slightly Compressible Modules

Samruam Baupradist, Phatsarapa Janmuang, Suphawat Asawasamrit

Abstract


In this paper, we give a generalization of slightly compressible modules. We introduce the notion of M-slightly compressible modules, i.e. a right R module N is called M-slightly compressible if for every nonzero submodule A of N there exists a nonzero R-homomorphism s from M to N such that . Many examples of M-slightly compressible modules are provided. Some results on M-slightly compressible modules are obtained, which are interesting and important.


Keywords


compressible modules; M-sightly compressible modules; slightly compressible modules

Full Text:

PDF

References


Wisbauer, R., Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, United States, 1991.

Anderson, F.W. & Fuller, K.R., Ring and Categories of Modules, Springer, New York, United States, 1974.

Kasch, F., Modules and Rings, London Math. Soc. Monographs 17(C.U.P.), 1982.

Zelmanowitz, J.M., An Extension of the Jacobson Density Theorem, Bull. Amer. Math. Soc., 82(4), pp. 551-553, 1976.

Khuri, S.M., The Endomorphism Ring of Nonsingular Retractable Modules, Bull. Aust. Math. Soc., 43(2), pp. 63-71, 1999.

Mcconnell, J.C. & Robson, J.C., Noncommutative Noetherian Ring, Wiley-Interscience, New York, United States, 1987.

Zhou, Z.P., A Lattice Isomorphism Theorem for Nonsingular Retractable Modules, Canad. Math. Bull., 37(1), pp. 140-144, 1999.

Smith, P.F., Modules with Many Homomorphisms, Journal of Pure and Applied Algebra, 197(1-3), pp. 305-321, 2005.

Baupradist, S. & Asawasamrit, S., On Fully-M-Cyclic Modules, Journal of Mathematics Research, 3(2), pp. 23-26, 2011.

Pandeya, B.M., Chaturvedi, A.K. & Gupta, A.J., Applications of Epiretractable Modules, Bulletin of the Iranian Mathematical Society, 38(2), pp. 469-477, 2012.

Lam, T.Y., Serre’s Problem on Projective Modules, Springer Verlag Berlin, Heidelberg, Germany, 2006.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2018.50.2.3

Refbacks

  • There are currently no refbacks.


View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

 

ITB Journal Publisher, LPPM ITB, Center for Research and Community Services (CRCS) Building, 6th & 7th Floor, Jalan Ganesha 10, Bandung 40132, Indonesia, Tel. +62-22-86010080, Fax.: +62-22-86010051; E-mail: jmfs@lppm.itb.ac.id