$\psi$-SECONDARY SUBMODULES OF A MODULE

Year 2020, Volume: 27 Issue: 27, 77 - 87, 07.01.2020

F. Farshadifar H. Ansari-toroghy

https://doi.org/10.24330/ieja.662963

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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