标题： 关于一些非交换dimonoid类 显示英文标题

标题： On some classes of non-commutative dimonoids

摘要： 本文致力于研究dimonoid，即具有两种满足特定公理系统的可结合二元运算的代数结构。我们探讨了对偶dimonoid的性质。在非交换dimonoid类中，我们构造了一些 Abel 群、非 Abel 群以及矩形 dimonoid。分析了这些对象的内部结构，特别是计算了它们的自同构群和光晕（halos）。 显示英文摘要

摘要： The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of non-commutative dimonoids, we construct a number of abelian, non-abelian, and rectangular dimonoids. The internal structure of these objects is analyzed, in particular, their automorphism groups and halos are computed.