فهرست نشریات علمی دسترسی آزاد ایران

Let $R$ be a commutative ring with identity. For $t\in N$, a proper submodule $N$ of an $R$-module $M$ is called a t-prime submodule if $rm\in N~(r\in R, m\in M)$, then $m\in N$ or $r^t\in (N:_RM)$. We obtain some other characterizations of t-prime submodules. Also by some other notions like t-secondary submodules, various properties of t-prime submodules are investigated. To this end, we deal with irreducible as well as reduced t-prime decompositions of a submodule. We provide several examples with illustrate our results.