Groups, rings, and algebras: common strategic approaches and mutual influences

Authors

  • M. Dixon University of Alabama, Tuscaloosa, USA
  • M. Semko State Tax University, Irpin, Kyiv region
  • I. Subbotin National University, Los Angeles, USA

DOI:

https://doi.org/10.3842/umzh.v78i1-2.8953

Keywords:

algebra, brace, group, ring, module

Abstract

UDC 512.5

We focus on recent promising trends in the application of the key concepts and approaches from the classical infinite-group theory to various branches of algebra, such as modules over group rings, infinite-dimensional linear groups, Leibniz algebras, other generalizations of the Lie algebras, and braces. The efficacy of these trends has been well-documented in a series of recent books from reputable publishers. In our article, we present a concise overview of these emerging trends. The analysis of the mutual influence of algebraic systems promotes deeper understanding of their individual and collective significance and illustrates the unity and diversity typical of contemporary mathematics. We believe that the subsequent development of investigations in this field would promote the appearance of new discoveries and innovations clarifying the fundamental role played by the groups, rings, algebras and other algebraic structures  in modern mathematics.

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Published

26.01.2026

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Vol. 78 No. 1-2 (2026)

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Research articles

How to Cite

Dixon, M., et al. “Groups, Rings, and Algebras: Common Strategic Approaches and Mutual Influences”. Ukrains’kyi Matematychnyi Zhurnal, vol. 78, no. 1-2, Jan. 2026, pp. 38–46, https://doi.org/10.3842/umzh.v78i1-2.8953.