t-PRIME SUBMODULES AND THEIR DECOMPOSITIONS

Let R be a commutative ring with identity. For t∈ N, a proper submodule N of an R-module M is called a t-prime submodule if rm∈ N~(r∈ R, m∈ M), then m∈ N or rᵗ∈ (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.