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MEANDERS IN ORTHOPOSETS AND QMV ALGEBRAS

MEANDERS IN ORTHOPOSETS AND QMV ALGEBRAS DEMONSTRATIO MATHEMATICAVol. XXXIVNo 12001A. Dvurecenskij, S. Pulmannova, S. SalvatiMEANDERS IN ORTHOPOSETS A N D QMV ALGEBRASA b s t r a c t . The notion of a meander of an ideal in lattices is generalized in two directions: to ideals in orthoposets and to ideals in QMV-algebras, and used to a characterization of subclasses of the above structures, namely Boolean orthoposets and QMV-algebrasin which every ideal is closed under perspectivity, and to a characterization of Riesz idealsin orthoposets and perspectivity closed ideals in QMV algebras.1. IntroductionThe notion of meanders of ideals in lattices was introduced by Beran[Bl] and further studied, e.g.,in [B2], [B,S]. The last mentioned paper dealswith meanders in ortholattices and orthomodular lattices.In the present paper, we generalize the notion of meanders to orthoposetsand to QMV-algebras.Orthoposets can be considered as algebraic structures with a partiallydefined binary operation - supremum of orthogonal elements. A subclassof orthoposets, orthomodulax posets, can be considered as a subclass ofeffect algebras, resp. difference posets ([FB], [KCh]. Ideals and congruencesin effect algebras (or, more generally, in partial abelian semigroups, resp.monoids) have been studied in [W], [P], [G,P], [Ch,P].QMV-algebras were introduced by Giuntini [Gi] as a (total) algebraicstructure which contains both orthomodular lattices and MV-algebras http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

MEANDERS IN ORTHOPOSETS AND QMV ALGEBRAS

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Publisher
de Gruyter
Copyright
© by A. Dvurečenskij
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2001-0102
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXXIVNo 12001A. Dvurecenskij, S. Pulmannova, S. SalvatiMEANDERS IN ORTHOPOSETS A N D QMV ALGEBRASA b s t r a c t . The notion of a meander of an ideal in lattices is generalized in two directions: to ideals in orthoposets and to ideals in QMV-algebras, and used to a characterization of subclasses of the above structures, namely Boolean orthoposets and QMV-algebrasin which every ideal is closed under perspectivity, and to a characterization of Riesz idealsin orthoposets and perspectivity closed ideals in QMV algebras.1. IntroductionThe notion of meanders of ideals in lattices was introduced by Beran[Bl] and further studied, e.g.,in [B2], [B,S]. The last mentioned paper dealswith meanders in ortholattices and orthomodular lattices.In the present paper, we generalize the notion of meanders to orthoposetsand to QMV-algebras.Orthoposets can be considered as algebraic structures with a partiallydefined binary operation - supremum of orthogonal elements. A subclassof orthoposets, orthomodulax posets, can be considered as a subclass ofeffect algebras, resp. difference posets ([FB], [KCh]. Ideals and congruencesin effect algebras (or, more generally, in partial abelian semigroups, resp.monoids) have been studied in [W], [P], [G,P], [Ch,P].QMV-algebras were introduced by Giuntini [Gi] as a (total) algebraicstructure which contains both orthomodular lattices and MV-algebras

Journal

Demonstratio Mathematicade Gruyter

Published: Jan 1, 2001

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