The concepts of higher Bi- homomorphism and Jordan higher Bi- homomorphism have been introduced and studied the relation between Jordan and ordinary higher Bi- homomorphism also the concepts of Co- higher Bi- homomorphism and  Co- Jordan higher Bi- homomorphism introduced  and the relation between them in Banach algebra have also been studied.

In this paper we introduce new class of open sets called weak N-open sets and we study the relation between N-open sets , weak N-open sets and some other open sets. We prove several results about them. 

    In this paper, the concepts of -sequence prime ideal and -sequence quasi prime ideal are introduced. Some properties of such ideals are investigated. The relations between -sequence prime ideal and each of primary ideal, -prime ideal, quasi prime ideal, strongly irreducible ideal, and closed ideal, are studied. Also, the ideals of a principal ideal domain are classified into quasi prime ideals and -sequence quasi prime ideals.

In this paper we introduce the idea of the commutator of two fuzzy subsets of a group and study the concept of the commutator of two fuzzy subsets of a group .We introduce and study some of its properties .

The aim of this research is to prove the idea of maximum m_X-N-open set, m-N-extremally disconnected with respect to t and provide some definitions by utilizing the idea of m_X-N-open sets. Some properties of these sets are studied.

The multiplicity of connotations in any paper does not mean that there is no main objective for that paper and certainly one of these papers is our research the main objective is to introduce a new connotation which is type-2 fuzzy somewhere dense set in general type-2 fuzzy topological space and its relationship with open sets of the connotation type-2 fuzzy set in the same space topology and theories of this connotation.

 The preparation of some new coordination compounds for nikel (II), manganese (II), copper (II), cobalt (II)and mercury (II), with ligand obtained from Benzoinand2-amino pyridine.The ligand[6-(2-hydroxy-1,2-diphenylethylideneamino)pyridin-3-ylium)](L) was made from reactin ethanol with metal salts in (1:1)(metal : ligand)ratio.[MLCl] was the inclusive formula of the complexes where M= Mn(II),Co(II),Ni(II),Cu(II) and Hg(II). Metal analysis by electronic spectra, atomic absorption ,infrared spectra, 1H&13C-NMR(only ligand)spectral studies, magnetic moment and molar conductance measurements used to describe the compounds.The determinations indicated that the ligand coordinates with the metal (II) ion in neutral tridentate manner th

    The main objective of this research is to study and to introduce a concept of strong fully stable Banach -algebra modules related to an ideal.. Some properties and characterizations of full stability are studied.

The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz

    In this study, the concept of fuzzy α-topological vector space is introduced by using the concept  fuzzy α-open set , some properties of fuzzy α-topological vector spaces are proved .We also show that the space is -space iff every singleton set is fuzzy α- closed .Finally, the convex property and its relation with the interior points are discussed.