FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 3, PAGES 113-118

On linear representations of quasigroups

A. A. Gvaramia
B. I. Plotkin

Abstract

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For homotopies of quasigroups, an analog of the fundamental theorem on homomorphisms does not hold in general. In this paper, we consider two approaches that allow one to obtain some analog of this theorem: the introduction of strict homotopies and the move from quasigroups to three-sorted quasigroups.

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