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AAA76 - 76th Workshop on General Algebra (76. Arbeitstagung Allgemeine Algebra)
May 22-25, 2008
Department of Algebra, Johannes Kepler University Linz
Linz, Austria

Organizers
Erhard Aichinger, Peter Mayr, Matt Nickodemus, Günter Pilz

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Existence and smearing theorem of states on atomic lattice effect algebras
by
Zdenka Riečanová
Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, SK-812 19 Bratislava, Slovak Republic

Existence and smearing theorem of states on atomic lattice effect algebras

Existence and smearing theorem of states on atomic lattice effect algebras

Zdenka Riecanová

It is well known that there exists even finite lattice effect algebras admitting no states (e.g.the well known Greechie's example of finite orthomodular lattice admitting no states). On the other hand, for instance, every interval effect algebra admits at least one state. Further, on every irreducible complete atomic modular lattice effect algebra there exists a faithful sate. We present further families of effect algebras possessing states, order-continuous states, or order-continuous subadditive states (valuations). Moreover, we present some families of lattice effect algebras for which the existence of an order-continuous state on sharp element implies the existence of a state on the whole effect algebra.


Acknowledgments The research was supported by grant G-3025/06 of MS SR and project APVV-0071-06.

References

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Riecanová, Z. (2008), Effect Algebraic Extensions of Generalized Effect Algebras and Two-Valued States. Fuzzy Sets and Systems 159, 1116-1122.

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Riecanová, Z., The Existence of States on Every Archimedean Atomic Lattice Effect Algebra with at Most Five Bloks. Kybernetika, to appear.

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Riecanová, Z. and Wu, J. (2008), States on Sharply Dominating Effect Algebras. Science in China Series A: Mathematics 51 No. 5, 907-914.

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Paseka, J. and Riecanová, Z., States on s-Compactly Generated Atomic Lattice Effect Algebras. Preprint.

Date received: May 12, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawc-56.