Khaldoun Al-Zoubi

Prime Submodules of Graded Modules

Let G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Reand g G G. In this article, we defineMg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we introduce a situation where if N is a gr-prime R-submodule of M ,then (Ng : Mg) is a maximal ideal of Re. We close this article by introducing a situation where if N is a gr- R-submodule ofM such that Ne is a weakly prime Re-submodule ofMe,thenNg is a prime Re-submodule of Mg.

Some properties of graded comultiplication modules

Abstract Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.

General numerical radius inequalities for matrices of operators

Abstract Let Ai ∈ B(H), (i = 1, 2, ..., n), and T=[ 0 ⋯ 0 A 1 ⋮ ⋰ A 2 0 0 ⋰ ⋰ ⋮ A n 0 ⋯ 0 ]

Numerical radius inequalities for Hilbert space operators

T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right]

On graded classical primary submodules

. In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.

On graded P-compactly packed modules

In this article, we give several inequalities involving powers numerical radii and the usual operator norms of Hilbert space operators. In particular, if Ai , Bi and Xi are bounded linear operators (i = 1,2, · · · ,n ∈ N) , then we estimate the norm as well as the numerical radius to ∑i=1 XiAi Bi for some m ∈ N .

On Graded Quasi-Prime Submodules

Abstract Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded classical primary submodules. Various properties of graded classical primary submodules are considered.

Some properties of graded 2-prime submodules

Abstract Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded P-compactly packed modules and we give a number of results concerning such graded modules. In fact, our objective is to investigate graded P-compactly packed modules and examine in particular when graded R-modules are P-compactly packed. Finally, we introduce the concept of graded finitely P-compactly packed modules and give a number of its properties.

On Graded Primary Ideals

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded quasi-prime submodules and give some basic results about graded quasi-prime submodules of graded modules. Special attention has been paid, when graded modules are graded multiplication, to find extra properties of these submodules. Furthermore, a topology related to graded quasi-prime submodules is introduced.

ON GRADED 2-ABSORBING AND WEAKLY GRADED 2-ABSORBING SUBMODULES

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded 2-prime submodule and we give a number of results concerning such modules. Also, we introduce and prove the graded 2-prime avoidance theorem for graded modules.