Theoretical Foundations of Applied Discrete Mathematics

Medial and paramedial alebras with strong dependable operations

A. V. Cheremushkin

Academy of Cryptography of Russian Federation

Abstract: We consider general functional medial and paramedial equations with four object variables. We give analogous results to those known for quasigroup operations for a class of strongly dependable operations. As a consequence of these results analogous linear representation for every operation of a binary algebra satisfying one of these hyperidentities is obtained.

Keywords: $n$-ary quasigroup, strong dependant operation, medial and paramedial operations.

UDC: 519.719.1

DOI: 10.17223/2226308X/17/5