Generalization of Slightly Compressible Modules


  • Samruam Baupradist Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330
  • Phatsarapa Janmuang Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330
  • Suphawat Asawasamrit Department of Mathematics, Faculty of Applied Science, King Mongkut??s University of Technology North Bangkok, Bangkok 10800



compressible modules, M-sightly compressible modules, slightly compressible modules


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.


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.