A few notes on subalgebra lattices. II
type: Item
instance of: scholarly article
zbMATH Open document ID: 0982.08001
author: Konrad Pióro
publication date: 2002-03-25T00:00:00Z
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08A55
Mathematics Subject Classification ID: 08A60
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 1619020
zbMATH Keywords: strong subalgebra lattice
zbMATH Keywords: weak subalgebra lattice
zbMATH Keywords: partial monounary algebra
MaRDI profile type: Publication
title: A few notes on subalgebra lattices. II
published in: Demonstratio Mathematica
review text: [For Part I see ibid. 33, No. 4, 695-706 (2000; Zbl 0970.08003).]NEWLINENEWLINENEWLINEIn 1990, W. Bartol characterized a lattice which is isomorphic to the lattice \(S_w(A)\) of all weak subalgebras of a given partial algebra \(A\). The author gives a simpler and shorter new proof of Bartol's theorem and then he modifies the conditions occurring in the theorem in order to obtain a characterization of \(S_w(A)\) for some partial monounary algebra \(A\) and some total monounary algebra \(A\). Further, he characterizes also the lattice \(S_s(A)\) of all strong subalgebras of these algebras. Moreover, he describes all pairs of lattices \((L_1,L_2)\) for which there exists a partial monounary algebra \(A\) such that \(S_w(A)\) or \(S_s(A)\) is isomorphic to \(L_1\) or \(L_2\), respectively.
reviewed by: Ivan Chajda
description: scientific article; zbMATH DE number 1619020