The second spectrum Specs (M) is the collection of all second elements of M. In this paper,
we study the topology on Specs (M), which is a generalization of the Zariski topology on the …

Let M be a left R-module. The set of all prime submodules of M is called the spectrum of M
and denoted by Spec (RM), and that of all prime ideals of R is denoted by Spec (R). For …

In this paper, we extend the definition of weakly second submodule of a module over a
commutative ring to a module over an arbitrary ring. First, we investigate some properties of …

Let G be a group with identity e. Let R be a G-graded commutative ring and let M be a
graded R-module. The graded classical prime spectrum Cl. Spec g (M) is defined to be the …

Here, we continue to characterize a recently introduced notion, le-modules RM over a
commutative ring R with unity [AK Bhuniya and M. Kumbhakar, Uniqueness of primary …

In this work, we study strongly prime submodules and strongly 0-dimensional modules. We
give some equivalent conditions for being a strongly 0-dimensional module. Besides we …

It is shown that the well-known characterizations of when a commutative ring R has
Noetherian spectrum carry over to characterizations of when the set Spec (M) of prime …

ABSTRACT A commutative ring R with identity satisfies the S-Noetherian spectrum
condition, where S⊆ R is a given multiplicative set, if for each ideal I of R, s I⊆ J⊆ I for some …

Let R be a commutative ring with identity and let M be an R-module. We examine the
situation where for each prime ideal ρof R the set of all ρ-prime submodules of M is finite. In …