%0 Journal Article %T Some remarks on generalizations of classical prime submodules %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Zolfaghari, Masoud %A Moslemi Koopaei, Mohammad Hosein %D 2019 %\ 11/01/2019 %V 6 %N 2 %P 67-80 %! Some remarks on generalizations of classical prime submodules %K $psi$-prime ideal %K $phi$-prime submodule %K n)$-$psi$-prime ideal %K $(n-1 %K n)$-$phi$-prime submodule %K $phi$-classical prime submodule %R 10.22034/as.2019.1485 %X Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $\phi:S(M)\rightarrow S(M)\cup \lbrace\emptyset\rbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$\phi$-classical prime submodule, if whenever $r_{1},\ldots,r_{n-1}\in R$ and $m\in M$ with $r_{1}\ldots r_{n-1}m\in N\setminus\phi(N)$, then $r_{1}\ldots r_{i-1}r_{i+1}\ldots r_{n-1}m\in N$, for some $i\in\lbrace 1,\ldots, n-1\rbrace$ $(n\geqslant 3)$.In this work, $(n-1, n)$-$\phi$-classical prime submodules are studied and some results are established. %U https://as.yazd.ac.ir/article_1485_0e20932e679114025d09ee6dffa7ca10.pdf