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

10.29252/as.2020.1786

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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