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ArticleOriginal scientific text

Title

Orthorings

Authors 1, 2

Affiliations

  1. Palacký University, Olomouc, Department of Algebra and Geometry, Tomkova 40, 77900 Olomouc, Czech Republic
  2. Vienna University of Technology, Institute of Discrete Mathematics and Geometry, Research Unit Algebra, Wiedner Hauptstraß e 8-10, 1040 Vienna, Austria

Abstract

Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.

Keywords

ENG
ortholattice, generalized ortholattice, sectionally complemented lattice, orthoring, arithmetical variety, weakly regular variety, congruence kernel, ideal term, basis of ideal terms, subtractive term

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Discussiones Mathematicae - General Algebra and Applications
2004/24/1
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Pages:
137-147
Main language of publication
English
Received
2004-03-02
Accepted
2004-06-09
Published
2004

DOI: 10.7151/dmgaa.1081

Exact and natural sciences