Document Type : Research Paper
Authors
University of Tikrit - College of Education
10.37652/juaps.2015.124476
Abstract
Let R be a commutative ring with identity, and let M be a unitary left R-module. In this work, we introduce quasi cancellation R-module (weakly quasi cancellation R-module) concept as a generalization of cancellation R-module (weakly cancellation R-module) concept we generalize some properties of cancellation (weakly cancellation) R-modules to quasi cancellation (weakly quasi cancellation) R-modules. Furthermore, we give some conditions under which R-module M is quasi cancellation R-module.
Keywords
Main Subjects
1- Burton , D. M. , Abstract and linear Algebra , Univ. of New Hampshire , (1971) .
2- David , D. and Richard F. , Abstract Algebra , Prentice Hall , (1991) .
3- David , M. Burton , Introduction to Modern Abstract Algebra , Addison - Wesley company , (1972) .
4- Ebrahimi Atai, S. Submodules of Multiplication Modules , TAIWANESE Journal of Mathematics , 9(3) , 385-396 , (2005) .
5- Fieldhouse , D. J. , pure theories , Math. Ann. 184:1-18 ,(1969).
6- Frank ,W. Anderson kent R. Fuller , Rings and Categories of Modules , springer -Verlag , Berlin , Heidelberg , New York , (1974) .
7- Gilmer R. W. , the Cancellation Law for Ideals in Comm. Ring , Canada J. math. , 17 : 281-287 , (1965) .
8- Heinzer, W.J., Ratliff L. J. And Rush , D.E. , Strongly Irreducible ideals of a Commutative Ring , J. Pure Appl Algebra , 166 , 267-275 , (2002).
9- Kasch F., Modules and Rings, Academic press, London, New York, (1982) .
10- Lambek J. , Lectures on Rings and Modules , Toronto , Blasdell publ. company , (1966) .
11- Larsen M. D. and Maccar P. J. , Multiplication Theory of Ideals , Academic press , London , New York , (1971) .
12- Mijbass , A. S. , On Cancellation Modules , M. SC. Thesis , college of science University of Baghdad , (1992) .
13- Smith P. F. , Some Remarks on Multiplication Modules , Arch. math. , 50 : 223-235 , (1988) .
14- Zaheb L. A. , Fazzy Sets , Information and control , 8 : 338-353 , (1965) .
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