Montaser I Adwan’s scientific contributions

Many new notions have been provided in the area of differential algebra and each one of them has been considered specific algebraic structure. In this paper, new notion on near-rings has been introduced. This notion is called generalized right-(1 , 2)-n-derivations of near-rings with some of its properties. The commutative property of such rings has been proved by using this notion.

Ring theory is one of the branches of an abstract algebra. This field is the study of a mathematical system with two binary operations. In this branch, many articles have studied this algebraic structure and presented some new works. However, the concept of purity has been studied before more than 40 years ago, especially the relation between the pure ideal and some other ideals on the given ring. In this paper, we survey the important results that concern with pure ideals. Some different types of ideals have been discussed such as N-pure ideals, z-ideals, Π-pure ideals and strongly pure ideals. Moreover, some recent results based on the work of several researchers have been summarized. On the other hand, regarding these types of ideals, some questions have been presented. Furthermore, many important results about various types of rings which are based on the notion of pure ideals have been studied.

Extended on the concept of projective product of semi-rings.

Many studies have been investigated the notation of differential algebra by considering some algebraic structures such as ring or semi-ring in order to study some of its properties. In this article, the results of [14] have been extended by introducing the notation of (,)-Ŝ-derivation pair and studied some properties of it. Furthermore, some examples are given to show that any (,)-Ŝ-derivation pair is a Jordan (,)-Ŝ-derivation pair but in general not conversely.

The concept of fuzzy set (FS) is one of the beautiful branches in Mathematics. This concept was initiated by Zadeh [1]. Since that time, many studies have been considered this concept by different ways in the field of pure and applied Mathematics. In this article, we introduced the notion of FT and FM on a D-algebras where FT is a fuzzy Translation and FM is a fuzzy Multiplication. We proved some characterizations of FT and FM of sub-algebra and d-ideal of a D-algebras Moreover, the notion of FM-αλ-T has been investigated on the D-algebras Furthermore, some results on the d-homomorphism of FT and FM which based on the fuzzy d-ideal of a D-algebras are presented.