Author/Authors :
Ansari-Toroghy, Habibollah Department of pure Mathematics - Faculty of mathematical Sciences - University of Guilan, Rasht, Iran , Farshadifar, Faranak Department of Mathematics - Farhangian University, Tehran, Iran , Mahboobi-Abkenar, Farideh Department of pure Mathematics - Faculty of mathematical Sciences, University of Guilan, 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.
