nach oben

Soft Computing

Erschienen in:

22.10.2015 | Foundations

Riesz decomposition properties and the lexicographic product of po-groups

verfasst von: Anatolij Dvurečenskij

Erschienen in: Soft Computing | Ausgabe 6/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We establish conditions when a certain type of the Riesz decomposition property (RDP) holds in the lexicographic product of two po-groups. It is well known that the resulting product is an \(\ell \)-group if and only if the first one is linearly ordered and the second one is an \(\ell \)-group. This can be equivalently studied as po-groups with a special type of the RDP. In the paper we study three different types of RDPs. RDPs of the lexicographic products are important for the study of pseudo effect algebras where infinitesimal elements play an important role both for algebras as well as for the first-order logic of valid but not provable formulas.

Vorheriger Artikel Pseudo equality algebras: revision

Nächster Artikel Design of granular interval-valued information granules with the use of the principle of justifiable granularity and their applications to system modeling of higher type

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Botur M, Dvurečenskij A (2015) Kite \(n\)-perfect pseudo effect algebras. Rep Math Phys (to appear). arXiv:1412.5434

Buhagiar D, Chetcuti E, Dvurečenskij A (2006) Loomis-Sikorski representation of monotone \(\sigma \)-complete effect algebras. Fuzzy Sets Syst 157:683–690MathSciNetCrossRefMATH

Cignoli R, D’Ottaviano IML, Mundici D (2000) Algebraic foundations of many-valued reasoning. Kluwer Academic Publishers, DordrechtCrossRefMATH

Darnel MR (1995) Theory of lattice-ordered groups. Marcel Dekker Inc, New YorkMATH

Diaconescu D, Flaminio T, Leuştean I (2014) Lexicographic MV-algebras and lexicographic states. Fuzzy Sets Syst 244:63–85. doi:10.1016/j.fss.2014.02.010 MathSciNetCrossRefMATH

Di Nola A, Grigolia R (2015) Gödel spaces and perfect MV-algebras. J Appl Log 13:270–284MathSciNetCrossRefMATH

Di Nola A, Lettieri A (1994) Perfect MV-algebras are categorical equivalent to abelian \(\ell \)-groups. Studia Logica 53:417–432MathSciNetCrossRefMATH

Dvurečenskij A (2002) Pseudo MV-algebras are intervals in \(\ell \)-groups. J Aust Math Soc 72:427–445MathSciNetCrossRefMATH

Dvurečenskij A (2007) Perfect effect algebras are categorically equivalent with Abelian interpolation po-groups. J Aust Math Soc 82:183–207MathSciNetCrossRefMATH

Dvurečenskij A (2010) Every state on interval effect algebra is integral. J Math Phys 51:083508–12. doi:10.1063/1.3467463 MathSciNetCrossRefMATH

Dvurečenskij A (2014) Representable effect algebras and observables. Int J Theor Phys 53:2855–2866. doi:10.1007/s10773-014-2083-z

Dvurečenskij A (2015a) How do \(\ell \)-groups and po-groups appear in algebraic and quantum structures? In: Montagna F et al (eds) Petr Hájek on mathematical fuzzy logic. Outstanding contributions to logic, vol 6. Springer, Berlin, pp 177–206. doi:10.1007/978-3-319-06233-4-9. ISBN 978-3-319-06232-7

Dvurečenskij A (2015b) Lexicographic effect algebras. Algebra Universalis (to appear)

Dvurečenskij A, Kolařík M (2014) Lexicographic product vs \(\mathbb{Q}\)-perfect and \(\mathbb{H}\)-perfect pseudo effect algebras. Soft Comput 17:1041–1053. doi:10.1007/s00500-014-1228-6 CrossRefMATH

Dvurečenskij A, Krňávek J (2013) The lexicographic product of po-groups and \(n\)-perfect pseudo effect algebras. Int J Theor Phys 52:2760–2772. doi:10.1007/s10773-013-1568-5 MathSciNetCrossRefMATH

Dvurečenskij A, Pulmannová S (2000) New trends in quantum structures. Kluwer Academic Publishers/Ister Science, Dordrecht/BratislavaCrossRefMATH

Dvurečenskij A, Vetterlein T (2001a) Pseudoeffect algebras. I. Basic properties. Int J Theor Phys 40:685–701MathSciNetCrossRefMATH

Dvurečenskij A, Vetterlein T (2001b) Pseudoeffect algebras. II. Group representation. Int J Theor Phys 40:703–726CrossRefMATH

Dvurečenskij A, Vetterlein T (2003) On pseudo-effect algebras which can be covered by pseudo MV-algebras. Demonstr Math 36:261–282MathSciNetMATH

Foulis DJ, Bennett MK (1994) Effect algebras and unsharp quantum logics. Found Phys 24:1331–1352MathSciNetCrossRefMATH

Fuchs L (1963) Partially ordered algebraic systems. Pergamon Press, OxfordMATH

Georgescu G, Iorgulescu A (2001) Pseudo-MV algebras. Multi Valued Log 6:95–135MathSciNetMATH

Glass AMW (1999) Partially ordered groups. World Scientific, SingaporeCrossRefMATH

Goodearl KR (1986) Partially ordered abelian groups with interpolation. Mathematical surveys and monographs, vol 20. American Mathematical Society, Providence

Pulmannová S (2002) Compatibility and decomposition of effects. J Math Phys 43:2817–2830MathSciNetCrossRefMATH

Rachůnek J (2002) A non-commutative generalization of MV-algebras. Czechoslov Math J 52:255–273

Ravindran K (1996) On a structure theory of effect algebras. PhD thesis, Kansas State University, Manhattan, Kansas

Riečanová Z (2000) Generalization of blocks for D-lattice and lattice ordered effect algebras. Int J Theor Phys 39:231–237MathSciNetCrossRefMATH

Titel: Riesz decomposition properties and the lexicographic product of po-groups
verfasst von: Anatolij Dvurečenskij
Publikationsdatum: 22.10.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 6/2016
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-015-1903-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 6/2016

Immune clonal selection algorithm for capacitated arc routing problem

Uniform adaptive scaling of equality and inequality constraints within hybrid evolutionary-cum-classical optimization

Genetic algorithms in wireless networking: techniques, applications, and issues

Stopping criteria for MAPLS-AW, a hybrid multi-objective evolutionary algorithm

Adaptive memetic algorithm for minimizing distance in the vehicle routing problem with time windows

Modeling and solving a capacitated stochastic location-allocation problem using sub-sources