The secondary radicals of submodules

Document Type : Research Paper

Authors

1 Department of pure Mathematics , Faculty of mathematical Sciences, University of Guilan, Rasht, Iran

2 Department of Mathematics, Farhangian University, Tehran, Iran

3 Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P. O. Box 41335-19141, Rasht, Iran

Abstract

Let R be a commutative ring with identity and let M be an R-module. In this paper, we will introduce the secondary radical of a submodule N of M as the sum of all secondary submodules of M contained in N, denoted by sec(N), and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual of primary radicals of submodules of M.

Keywords


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