Notes on reduced, artinian and multiplication modules

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, P.O.Box 56199-11367, Ardabil, Iran.

2 Department of Mathematics, Sosangerd Branch, Islamic Azad University , Sosangerd, Iran.

Abstract

Let M be a unitary module over a commutative ring R with identity. In this paper we consider the concepts of Artinian, semi-Artinian, reduced and multiplication modules . Also we call an R-module M radical, if it has no maximal submodule. By P(M) we denote the sum of the radical submodules of M and we show that P(M/(P(M)) = 0.

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References

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[4] Rudlof, P., On minimax and related modules, Can. J. Math. Vol. 44(1),(1992),154-166.
[5] Sharpe, D. W. and Vamos, P., Injective modules, (Lectures in pure Mathematics), University of sheffield, (1972). 
Journal of Hyperstructures
Volume 3, Issue 2
December 2014
Pages 108-115

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