This article is cited in 3 papers

Theoretical Backgrounds of Applied Discrete Mathematics

Medial and paramedial general identities for strong dependance operations

A. V. Cheremushkin

Academy of Cryptography of the Russian Federation, Moscow, Russia

Abstract: We consider general functional medial and paramedial equations with four object variables. We give analogous of khown results with quasigroup operations for a class of strong dependable operations. As a consequence of these results, an analogous linear representation for every operation of a binary algebra satisfying one of these hyperidentities is obtained. Nevertheless, co-medial and co-paramedial algebras may have nonlinear binary operations.

Keywords: $n$-ary quasigroup, strong dependent operation, medial and paramedial operations, linear representation.

UDC: 519.719.1

DOI: 10.17223/20710410/65/2