A functional identity of generalized transitivity for strongly dependent $n$-ary operations

A. V. Cheremushkin

Academy of Cryptography of Russian Federation

Abstract: We proof that functional identity of generalized transitivity for strongly dependent operations may be described in analogy with quasigroups by replacing term «group» by term «monoid». We show how to generalize this result to $n$-ary strongly dependent operations.

Keywords: binary and $n$-ary quasigroups, strongly dependent operation, generalized transitivity identity.

UDC: 512.548.7

Received: 18.09.2023

DOI: 10.4213/dm1796