Qualitative MR-groups and tensor performances

Examining infinite groups often faces serious difficulties due to the complexity of the object of study. Virtually every approach to studying infinite groups is either less effective or applicable only to narrow groups of groups.For example, the developing and highly powerful system of concepts and techniques of module theory in its classical form is applicable only to Abelian groups. It is therefore very important to spread the ideas and methods of module theory in the case of non-commutative groups. This shows the urgency of the topic of the master thesis. The master thesis is dedicated to the study of quality groups with respect to rings. This concept is introduced by R. By Lyndon about sixty years ago and has been studied by many authors. In the master thesis, qualitative groups with more convenient axioms will be studied, which clarifies R. Lyndon definition and proposed a. Miasnikov et al. By Remeslenikov. Qualitative group theory issues related to their general properties and their tensor performance (concepts related to scaling ring extensions for quality groups) are discussed. Key findings and novelties are included in the content and approvals of Theorem 6.2 and Theorem 6.3 (Section 2).

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