Infinite-dimensional quasigroups of finite orders.
type: Item
instance of: scholarly article
title: Infinite-dimensional quasigroups of finite orders.
zbMATH Open document ID: 1283.20071
DOI: 10.1134/S0001434613030152
published in: Mathematical Notes
publication date: 2013-07-08T00:00:00Z
review text: The paper continues the author's research on the characterization of infinite dimensional quasigroups of finite orders. The main result is that every quasigroup of order 4 is either semilinear or reducible (i.e. representable in the form of a superposition). Semilinear quasigroups have a characterization in terms of Boolean functions and reducible quasigroups can be represented by using their own retract.
Mathematics Subject Classification ID: 20N15
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 06E30
zbMATH DE Number: 6185223
zbMATH Keywords: \(n\)-quasigroups
zbMATH Keywords: reducible quasigroups
zbMATH Keywords: semilinear quasigroups
zbMATH Keywords: Boolean functions
zbMATH Keywords: Lebesgue nonmeasurable sets
author: Vladimir N. Potapov
MaRDI profile type: Publication
cites work: Q4767924
cites work: Q5437058
cites work: Q3792904
cites work: On reducibility of \(n\)-ary quasigroups
cites work: n-Ary Quasigroups of Order 4
description: scientific article; zbMATH DE number 6185223