TL;DR
This paper explores linear quasigroups and their generalizations, discussing foundational definitions, elementary properties, and the structure of endomorphisms and endotopies within these algebraic systems.
Contribution
It provides a comprehensive analysis of linear quasigroups, including new insights into their properties and the behavior of their endomorphisms and endotopies.
Findings
Elementary properties of linear quasigroups are established.
Endomorphisms and endotopies of linear quasigroups are characterized.
Generalizations of linear quasigroups are analyzed.
Abstract
The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and their generalizations are presented. Finally in the third part endomorphisms and endotopies of linear quasigroups and their generalizations are investigated.
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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · Optics and Image Analysis