arXiv subjects
Publications and source records attributed to Faraj. A. Abdunabi.
In this paper, we present the concepts of the upper and lower approximations of Anti-rough subgroups, Anti-rough subsemigroups, and homeomorphisms of Anti-Rough anti-semigroups in approximation spaces. Specify the concepts of rough in Finite anti-groups of types(4) are studies. Moreover, some properties of approximations and these algebraic structures are introduced. In addition, we give the definition of homomorphism anti-group.
We investigate and present a new result in NG groups that consisting of consisting of non-bijective transformations cannot be subset of symmetric groups. In this paper, we revive the concepts of NG groups. Moreover, we introduce the definition of regular NG and inverse NG the new concept as new results in these groups. Hover, some properties are studied.
This study was aimed to consider the NG-group that consisting of transformations on a nonempty set A has no bijection as its element. In addition, it tried to find the maximal order of these groups. It found the order of NG-group not greater than n. Our results proved by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A.
In this paper, we introduce and study the graph of the groups of mappings on a set X with respect to function compositions that cannot be subsets of the symmetric groups S3 and S4. Furthermore, we investigate some of the justifications on these groups that have studied in graph theory, and we got good results. Moreover, we consider the graph of these groups by fixed points and study some properties of it.
In this paper, we will be delving deeper into the connection between the rough theory and the ring theory precisely in the principle and maximal ideal. The rough set theory has shown by Pawlak as good formal tool for modeling and processing incomplete information in information system. The rough theory is based on two concepts the upper approximation of a given set is the union of all the equivalence classes, which are subsets of the set, and the lower approximation is the union of all the equivalence classes, which are intersection with set non-empty. Many researchers develop this theory and use it in many areas. Here, we will apply this theorem in the one of the most important branches of mathematics that is ring theory. We will try to find the rough principal and maximal ideal as an extension of the notion of a principal maximal ideal respectively in ring theory. In addition, we study the properties of the upper and lower approximation of a principal maximal ideal. However, some researchers use the rough theory in the group and ring theory. Our work, is Shaw there are rough maximal and principle ideal as an extension of the maximal and principle ideal respectively. Our result will introduce the rough maximal ideal as an extended notion of a classic maximal ideal and we study some properties of the lower and the upper approximations a maximal ideal.
In this paper, we introduce the upper and lower approximations on the invers set-valued mapping and the approximations an established on a powerful set valued homomorphism from a ring R1 to power sets of a ring R2. Moreover, the properties of lower and upper approximations of a powerful set valued are studies. In addition, we will give a proof of the theorem of isomorphism over approximations F-rough ring as new result. However, we will prove the kernel of the powerful set-valued homomorphism is a subring of R1. Our result is introduce the first isomorphism theorem of ring as generalized the concept of the set valued mappings.