SUPPLEMENTS IN COATOMIC MODULES HAVING THE COMPLETE MAX-PROPERTY

Year 2018, Volume: 24 Issue: 24, 18 - 30, 05.07.2018

Mame Demba Cisse Lamine Ngom Djiby Sow Rachid Tribak

https://doi.org/10.24330/ieja.440141

https://izlik.org/JA22TB27SG

Abstract

Let R be a ring with identity. A right R-module M has the com-

plete max-property if the maximal submodules of M are completely coindepen-

dent (i.e., every maximal submodule of M does not contain the intersection

of the other maximal submodules of M). A right R-module is said to be a

good module provided every proper submodule of M containing Rad(M) is an

intersection of maximal submodules of M. We obtain a new characterization

of good modules. Also, we study good modules which have the complete max-

property. The second part of this paper is devoted to investigate supplements

in a coatomic module which has the complete max-property.

Keywords

Coatomic module , completely coindependent , complete max- property , good module , maximal submodule

References

• G. F. Birkenmeier, F. Takil Mutlu, C. Nebiyev, N. Sokmez and A. Tercan, Goldie*-supplemented modules, Glasg. Math. J., 52(A) (2010), 41-52.
• E. Buyukasik and D. Pusat-Yilmaz, Modules whose maximal submodules are supplements, Hacet. J. Math. Stat., 39(4) (2010), 477-487.
• M. D. Cisse and D. Sow, On generalizations of essential and small submodules, Southeast Asian Bull. Math., 41(3) (2017), 369-383.
• J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkhauser Verlag, Basel, 2006.
• C. Nebiyev and A. Pancar, On supplement submodules, Ukrainian Math. J., 65(7) (2013), 1071-1078.
• P. F. Smith, Module with coindependent maximal submodules, J. Algebra Appl., 10(1) (2011), 73-99.
• R. Wisbauer, Foundations of Module and Ring Theory, Algebra, Logic and Applications, 3, Gordon and Breach Science Publishers, Philadelphia, PA, 1991.
• H. Zoschinger, Koatomare moduln, Math. Z., 170(3) (1980), 221-232.