ON REDUCED MODULES

Year 2009, Volume: 58 Issue: 1, 9 - 16, 01.02.2009

N. Agayev S. Halıcıoğlu A. Harmancı

https://doi.org/10.1501/Commua1_0000000642

Cited By: 1

Abstract

Abstract. Let α be an endomorphism of an arbitrary ring R with identity.
In this note, we concern the relations between polynomial and power series
extensions of a reduced module. Among others we prove that a ring R is α-
reduced if and only if every áat right R-module is -reduced, and for a module
M, M[x] is α-reduced if and only if M[x; x1
] is α-reduced.

Keywords

reduced modules

References

• N. Agayev and A. Harmanci, On semicommutative modules and rings, Kyungpook Math. J., 47(2007)(1), 21-30.
• F.W. Anderson and K.R. Fuller, Rings and categories of modules, Springer-Verlag, New York, 1974.
• A.M. Buhphang and M.B. Rege, Semi-commutative module and Armendariz modules, Arab. J. Math. Sci., (8) (2002), 53-65.
• W.X. Chen and W.T. Tong, A note on skew Armendariz rings, Com. Algebra, 33 (2005), 1137-1140.
• C.Y. Hong, N.K. Kim and T.K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure and Appl. Algebra, 151 (3)(2000), 215-226.
• T.K. Lee and Y. Zhou, Reduced modules, Rings, modules, algebras, and abelian groups, 365– 377, Lecture Notes in Pure and Appl. Math., 236, Dekker, New York, 2004.
• C. Zhang and J. Chen, skew Armendariz modules and semicommu- tative modules, Tai wanese J. Math., 12 (2) (2008), 473-486.
• Current address :, N. Agayev: Department of Pedagogy, Qafqaz University, Baku, Azerbaijan
• S. Halıcıo¼glu: Department of Mathematics, Ankara University, Ankara, Turkey
• A.Harmanci: Department of Mathematics,Hacettepe University, Ankara, Turkey E-mail address : [e-mail], [e-mail]
• [e-mail]