Scholarlink

<p>We focus on new promising trends in the application of key concepts and approaches from the classical infinite-group theory to various branches of algebra, such as the modules over group rings, infinite-dimensional linear groups, Leibniz algebras, some other generalizations of Lie algebras, and braces. The efficiency of these trends has been well documented in a series of recent books from reputable publishers. We present a concise overview of recently emerging trends. The analysis of the mutual influence of algebraic systems promotes deeper understanding of their individual and collective significance and illustrates their 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 contemporary mathematics.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Groups, Rings, and Algebras: Common Strategic Approaches and Mutual Effects

  • 期刊论文

  • 发表日期：

    2026年5月22日

查看全文
  • Martyn Dixon,
  • Mykola Semko,
  • Igor Subbotin

摘要

We focus on new promising trends in the application of key concepts and approaches from the classical infinite-group theory to various branches of algebra, such as the modules over group rings, infinite-dimensional linear groups, Leibniz algebras, some other generalizations of Lie algebras, and braces. The efficiency of these trends has been well documented in a series of recent books from reputable publishers. We present a concise overview of recently emerging trends. The analysis of the mutual influence of algebraic systems promotes deeper understanding of their individual and collective significance and illustrates their 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 contemporary mathematics.