The secondary radicals of submodules

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.

کلیدواژه ها:

Secondary module ، completely irreducible submodule ، and secondary radical