This article is cited in 10 papers

Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent $n$-ary operations

A. V. Cheremushkin

Research Institute "Kvant", Moscow

Abstract: The paper contains an extension of Malyshev theorem for $n$-ary quasigroups with a right or left weak invertibility property to the case of strongly dependent $n$-ary operations. As a corollary a new proof of Gluskin–Hosszú theorem for strongly dependent $n$-ary semigroups is obtained.

Keywords: $n$-ary groups, strongly dependent operations, weak invertibility.

UDC: 512.538

Received: 05.03.2018
Revised: 19.04.2018

DOI: 10.4213/dm1508

 English version: Discrete Mathematics and Applications, 2019, 29:5, 295–302

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