Let MR be a module with S= End (MR). We call a submodule K of MR annihilator-small if K+
T= M, T a submodule of MR, implies that l (S)(T)= 0, where l (S) indicates the left annihilator …

Throughout this note, all rings are commutative and all modules are unitary. Let R be a ring
and M an R-module. We shall define the prime radical of M to be the intersection of M and all …

LetR be a commutative ring with unity and let N be a submodule of anon-zero left R-module
M, N is called prime if wheneverr x∈ N, r∈ R, x∈ M, implies that either x∈ N orr∈[N: M] …

Let R be a commutative ring with identity and N is a proper submodule of an R-module M. A
submodule N is said to be J-primary if whenever rx∈ N+ J (M) for some r∈ R, x∈ M and J …

Let R be a ring with identity and M be a unital right R-module. A nonzero submodule N of M
is called a second submodule if N and all its nonzero homomorphic images have the same …

Inspired by the interplay between the Zariski topology defined on the prime spectrum of a
commutative ring R and the ring theoretic properties of R in [3, 8, 18, 23, 25], we introduce in …

Let be a commutative ring with unity and let be a submodule of anon zero left R-module, is
called semiprime if whenever, implies. In this paper we say that is nearly semiprime, if …

Throughout this paper R represents a commutative ring with identity and all R-modules M
are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as …

Let; M be a unitary; left R-module on; associative ring with; identity; R. A submodule; K of M
is called; R-ann-small; if K+ T= M, where T is a submodule of M, implies that ann (T)= 0 …

Let R be a commutative ring and M be a Noetherian R-module. The intersection graph of
annihilator submodules of M, denoted by GA (M) is an undirected simple graph whose …