Quasi-Boolean powers of semilattices
type: Item
instance of: scholarly article
title: Quasi-Boolean powers of semilattices
zbMATH Open document ID: 1012.06005
author: V. N. Saliĭ
published in: Russian Mathematics
publication date: 2001-10-31T00:00:00Z
review text: This paper presents conditions for a groupoid to be embeddable into a quasi-Boolean power of a certain semilattice: Theorem. A groupoid \(G\) admits embedding into a quasi-Boolean power of a certain semilattice if and only if the following conditions hold: I. in \(G\) the identities \(xx=x\), \(xy=yx\), and \(x(xy)=xy\) are valid; II. on \(G\) there exists a congruence \(\theta\) all of whose classes are semilattices and the factor-groupoid \(G/\theta\) is also a semilattice; III. the relation \(\omega= \{(\alpha,\beta)\in G\times G\mid(\alpha,\beta)\in \theta\) and \(\alpha\beta= \alpha\}\) represents a stable order on \(G\).
reviewed by: Ladislav Skula
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 1541504
zbMATH Keywords: groupoid
zbMATH Keywords: quasi-Boolean power
zbMATH Keywords: semilattice
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541504