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.Specg(M) is defined to be the set of all graded classical prime submodule of M. The Zariski topology on Cl.Specg(M); denoted by ϱg. In this paper we establish necessary and sufficient conditions for Cl.Specg(M) with the Zariski topology to be a Noetherian...

Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...

Soil–reinforcement interaction is a major factor in the analysis and design of reinforced earth structures. In current research effects attaching elements different size numbers as anchors on enhancement at soil–geogrid interface under direct shear conditions were studied. Poorly well graded sands (SC & Sf), high density polyethylene geogrid, with three (layouts) clamping length 2 cm from surfa...

Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of classical strongly 2-absorbing second submodules modules over rings. A number results concerning these classes their homogeneous components are given.

the formulation of hydrophobic drugs for oral drug delivery is challenging due to poor solubility, poor dissolution and poor wetting of these drugs. consequently, the aim of this study was to improve the dissolution of a model poorly water soluble drug, ibuprofen. microparticles containing ibuprofen were produced by spray drying and spray chilling technology in the absence/presence of a hydroph...