Hyperidentities with permutations in invertible binary algebras

[摘要] In this paper, using hyperidentities with permutations we obtained characterization invertible algebras of various types of linearity.A binary algebra (Q; Σ) is called invertible algebra or system of quasigroups if each operation in Σ is a quasigroup operation. Invertible algebras with second-order formulas first were considered by Shaufler [17] in connection with coding theory. He pointed out that the resulting message would be more difficult to decode by an unauthorized receiver than in the case when a single operation is used for calculation. Later such algebras were investigated by J. Aczel [1], V. D. Belousov [3, 5], A. Sade [16], Yu. M. Movsisyan [11]– [15] and others.

[学科分类] 环境科学（综合）

[关键词] Invertible algebra;Second-order formula;Hyperidentity with permutations;Isotopy