Let R be an associative ring with identity and M be a unitary right R-module. A submodule N of M is called a uniformly primal submodule provided that the subset B of R is uniformly not right prime to N , if there exists an element s ∈ M − N with sRB ⊆ N .The set adj N = r ∈ R | mRr ⊆ N   for some  m ∈ M is uniformly not prime to N .This paper is concerned with the properties of uniformly primal submodules. Also, we generalize the prime avoidance theorem for modules over noncommutative rings to the uniformly primal avoidance theorem for modules.

Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If N N  α α∈Λ ⊆ where N α is a primary submodule of M for each α ∈ Λ , then i n i N N M  α 1 = + ≠ for some n α α α 1 2 , , , ∈ Λ . When there exists β ∈ Λ such that N N M β + ≠ ; N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.

In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.