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ArticleOriginal scientific text

Title

Semilattices with sectional mappings

Authors 1, 2

Affiliations

  1. Department of Algebra and Geometry, Palacký University of Olomouc Tomkova 40, 779 00 Olomouc, Czech Republic
  2. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10/104, 1040 Wien, Austria

Abstract

We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].

Keywords

ENG
semilattice, sectional mapping, antitone mapping, switching mapping, involution

Bibliography

  1. J.C. Abbott, Semi-Boolean algebras, Matem. Vestnik 4 (1967), 177-198.
  2. I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003, pp. 217.
  3. I. Chajda and P. Emanovský, Bounded lattices with antitone involutions and properties of MV-algebras, Discussiones Mathem., General Algebra and Appl. 24 (1) (2004), 31-42.
  4. I. Chajda, R. Halaš and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19-33.
Discussiones Mathematicae - General Algebra and Applications
2007/27/1
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Pages:
11-19
Main language of publication
English
Received
2006-02-16
Accepted
2006-04-27
Published
2007

DOI: 10.7151/dmgaa.1115

Exact and natural sciences