Study of Isomorphism Between Lattice Groups And Fuzzy Groups

The objective of this studying is the important answer on the following open question : Let G and G' be two fuzzy groups and L(G), L(G') be lattices for them, respectively, We have shown that this statement don’t true in the case general, and we suppose some certain conditions on the purposed groups to be the statement holds. Moreover, some important theorems are proved

Isomorphism-invariants and their applications in testing for isomorphism between finitely presented groups

This paper introduces some isomorphism-invariants for groups and uses them to test two finitely presented groups. The introduced algorithm starts with the construction of all cyclic groups contained in the groups under test, then it compares the distribution of a particular set of elements in the constructed cyclic groups. The algorithm leads to one of these two results: 1. The groups have the same "fingerprint" 2. The groups are not isomorphic

Developing Hilbert’s Nullstellensatz into Categorical Adjunction

This paper includes an improvement of the categorical isomorphism between the category of radical ideals and the category of affine algebraic sets into an adjunction between two functors. Afterwards, we extend the previous functors by means of expanding our work into the category of all ideals in a polynomial ring in n variables over a fixed algebraically closed field k, in which the radical ideals form a full subcategory of it, in order to produce more generalized adjunction.

New Properties for Inductive Isomorphisms of Groups

تتضمن الورقة العلمية نتائج مهمة تتكون من خواص جديدة للتماثلات الاستقرائية للزمر. وتتجلى الخواص الرئيسة الجديدة في نصوص كل من المبرهنة ( 6) و المبرهنة (7) و النتيجة (8) التي تم إثبات صحتها في هذا البحث، حيث تمت الإجابة عن أسئلة مفتوحة حول الجداء نصف المباشر و حول التماثل و حول مشتق الزمرة كخواص للتماثل الاستقرائي لزمرتين.

Criteria to Distinguish non-Isomorphism Hypergraphs

The paper aims to distinguish the couple-couple non-isomorphism hypergraphs, which have a known vertexes number, Z, and sides number, d. To solve this problem a number of criteria graded in distinguishing accuracy are developed. It also presents an experimental method to test the efficiency of the used criteria. It gives a method to put them in order. This research is considered a practical because it is useful in designing of machines and variable structure complex systems, and in comparing the new patterns.