‏a ‎generalization ‎of‎ ‎‎r‎-submodules ‎

Let r be a commutative ring with identity 1 ̸= 0 and m a non-zero unital r-module. in this paper, we present the concept of fully i-submodules of m such that i is an ideal of r which is a generalization of r-submodules. consider that i is an ideal of r, a proper submodule n of m is a fully i-submodule if jk ⊆ n with annm (j ) = 0m results that k ⊆ n for each submodule k of m and each ideal j of r. in addition, we present the concept of fully special i-submodules which is a generalization of special r-submodules. a proper submodule n of m is a fully special i-submodule if the inclusion il ⊆ n with annr(l) = 0r, implies that i ⊆ (n : m ) for each submodule l of m and each ideal j of r. we explore certain outcomes related to these categories of submodules.