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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
Demonstratio Mathematica – de Gruyter
Published: Jan 1, 2001
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