Some remarks on generalizations of classical prime submodules

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-۱, n)-\phi-classical prime submodule, if whenever r_{۱},\ldots,r_{n-۱}\in R and m\in M with r_{۱}\ldots r_{n-۱}m\in N\setminus\phi(N), then r_{۱}\ldots r_{i-۱}r_{i+۱}\ldots r_{n-۱}m\in N, for some i\in\lbrace ۱,\ldots, n-۱\rbrace (n\geqslant ۳).In this work, (n-۱, n)-\phi-classical prime submodules are studied and some results are established.

کلیدواژه ها:

psi-prime ideal ، phi-prime submodule ، n)-psi-prime ideal ، (n-۱ ، n)-phi-prime submodule ، phi-classical prime submodule