Images of simple lattice polynomials
type: Item
instance of: scholarly article
title: Images of simple lattice polynomials
zbMATH Open document ID: 0819.06005
DOI: 10.1007/BF01190762
author: Ivan Rival
author: Nejib Zaguia
published in: Algebra Universalis
publication date: 1995-02-22T00:00:00Z
review text: Having in mind some open problems about isotone self-maps of lattices, the authors prove the following two theorems, which are intended as steps for approaching the solution of these problems. (1) For any bounded ordered set there is a lattice and a polynomial of that lattice whose image is isomorphic to a subset isomorphic to this bounded ordered set. (2) For any elements \(a\), \(b\) in any lattice the image of the polynomial \((x+a)\cdot b\) is an order sublattice.
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 724099
zbMATH Keywords: lattice polynomial
zbMATH Keywords: isotone mapping
zbMATH Keywords: bounded ordered set
zbMATH Keywords: order sublattice
reviewed by: Ján Jakubík
MaRDI profile type: Publication
cites work: Über endliche, ordnungspolynomvollständige Verbände
cites work: On Prepolynomially Complete Algebras
cites work: Eine Charakterisierung endlicher, ordnungspolynomvollständiger Verbände
cites work: Über endliche, ordnungsaffinvollständige Verbände
description: scientific article; zbMATH DE number 724099