This article is cited in 8 papers

Partially invertible strongly dependent $n$-ary operations

A. V. Cheremushkin

Research Institute "Kvant", Moscow, Russia

Abstract: We prove analogues of Malyshev's theorems on the structure of finite $n$-quasigroups with the weak invertibility condition and of Belousov's theorem with a description of $(i,j)$-associative $n$-quasigroups for the case of strongly dependent $n$-ary semigroup operations on a finite set.
Bibliography: 8 titles.

Keywords: $n$-ary semigroup, strongly dependent operation, weakly invertible operation.

UDC: 512.53+512.548.2+512.548.4

MSC: Primary 20N15; Secondary 20N05

Received: 05.12.2018 and 04.07.2019

DOI: 10.4213/sm9204

 English version: Sbornik: Mathematics, 2020, 211:2, 291–308

Bibliographic databases:

• 
• 
• 
• 
• 
•