$\psi$-SECONDARY SUBMODULES OF A MODULE

Abstract

Let $R$ be a commutative ring with identity and $M$ be an $R$-module. Let $\psi : S(M)\rightarrow S(M) \cup \{\emptyset \}$ be a function, where $S(M)$ denote the set of all submodules of $M$. The main purpose of this paper is to introduce and investigate the notion of $\psi$-secondary submodules of an $R$-module $M$ as a generalization of secondary submodules of $M$.

Keywords

• Secondary submodule,phi-prime ideal,weak secondary submodule,psi-secondary submodule

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