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Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 137-147
DOI: https://doi.org/10.7151/dmgaa.1081

ORTHORINGS

Ivan Chajda Palacký University, Olomouc Department of Algebra and Geometry Tomkova 40, 77900 Olomouc, Czech Republic e-mail: chajda@inf.upol.cz

Helmut Länger Vienna University of Technology Institute of Discrete Mathematics and Geometry Research Unit Algebra Wiedner Hauptstraß e 8-10, 1040 Vienna, Austria e-mail: h.laenger@tuwien.ac.at

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

2000 Mathematics Subject Classification: 16Y99, 06C15, 81P10.

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Received 2 March 2004
Revised 9 June 2004