Semilattices with a group of automorphisms
type: Item
instance of: scholarly article
title: Semilattices with a group of automorphisms
zbMATH Open document ID: 0934.08001
published in: Algebra Universalis
publication date: 2000-02-27T00:00:00Z
full work available at URL: 1116606.pdf
review text: An algebra \({\mathcal S}=\langle S;\wedge ,F \rangle \) with a binary operation \(\wedge \) and a set \(F\) of unary operations is an \(\mathcal F\)-semilattice if \(\mathcal F = \langle F;\cdot ,{}^{-1},\text{id} \rangle \) is a group and \({\mathcal S}\) satisfies the following identities: (a) \(\wedge \) is a semilattice operation, (b) \(\text{id}(x)=x\), (c) \(f(g(x)) = (f\cdot g)(x)\) for all \(f,g\in F\), and (d) \(f(x\wedge y) = f(x)\wedge f(y)\) for all \(f\in F\). In other words, an \(\mathcal F\)-semilattice is a semilattice expanded with a set \(F\) of new operations which forms an automorphism group of the semilattice. The author describes up to isomorphism all simple algebras of \(\mathcal F\)-semilattices in the case when \(\mathcal F\) is commutative. An example of a simple algebra that does not fit in the previous description for non-commutative \(\mathcal F\) is given. This generalizes investigations by \textit{J. Ježek} [Algebra Univers. 15, 162-175 (1982; Zbl 0512.06006)].
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 08A35
zbMATH DE Number: 1407076
zbMATH Keywords: semilattice
zbMATH Keywords: automorphism group
zbMATH Keywords: expansion
zbMATH Keywords: simple algebra
author: M. Maróti
MaRDI profile type: Publication
OpenAlex ID: W2094109399
DOI: 10.1007/S000120050054
description: scientific article; zbMATH DE number 1407076