Document Type : Research Paper
Authors
College of Computer Science and Mathematics-Tikrit University
Abstract
"Throughout this paper R represents commutative ring with identity and M is unitary left R-module", the purpose of this paper is to study new concept (up to our knowledge) , named 2-maximal submodule which is a generalization of maximal submodule , "where a submodule N of an R-module M is called 2-maximal" submodul of M if and only if M/N is 2-regular R-module . Many characterizations and properties of 2-maximal submodules are given . Moreover we studied the behavior of 2-maximal submodule in some classes of module . Finally we give the sufficient condition 2-maximal submodules to be semi-maximal weak-maximal submodules are introduced .
Main Subjects
- Khalaf , H. Y. (( Semi-maximal Submodules )) , ph.D thesis , Univ. of Baghdad , 2007.
- Shwkaea M. R. (( Weak Maximal Ideals and Weak Maximal Submodules)) ,M.Sc. thesis , Univ, of Tikrit , 2012.
- Ghaleb , A. H. (( Generalization of Regular Modules and Pure Submodules )) , ph.D , thesis , Univ. of Baghdad , 2015.
- Desale , G. And Nicholson , W. (( Endoprimitive Rings )) J. Algebra , 70, 545-560 ,(1981).
- El-Bast , Z. A. And Smith , P.P. (( Multiplication Modules )) , Comm. In Algebra , 16 , 755-770 ,(1988).
- Goldie , K. R. (( Torsion Free Modules and Rings )) , J. Algebra , 1,268-287 , (1964).
- Mohammad ali H.K , Mohammod A.S. and Sallman M.D. (( 2-Maximal Ideals and 2-Maximal R-Modules )) ,To a paper.
- Lam , T. Y. (( Lecture on Modules and Rings )) , Berkely California , 1998
- Kasch , F. (( Modules And Rings )) Acad , Press., London , 1982.
- 10. Al-Aubaidy W. K. (( The Ring of Endomorphism of Multiplication Modules )) M.Sc. thesis , Univ. of Baghdad ,1993.
11. Sharide F.A((S-compactly packed submodules and Semi prime Modules)) , M.Sc. thesis Univ. of Tikrit , 2008.