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BY-NC-ND 3.0 license Open Access Published by De Gruyter November 15, 2014

States on bounded commutative residuated lattices

Michiro Kondo
From the journal Mathematica Slovaca

Abstract

We define states on bounded commutative residuated lattices and consider their property. We show that, for a bounded commutative residuated lattice X, (1)If s is a state, then X/ker(s) is an MV-algebra.(2)If s is a state-morphism, then X/ker(s) is a linearly ordered locally finite MV-algebra.

Moreover we show that for a state s on X, the following statements are equivalent: (i)s is a state-morphism on X.(ii)ker(s) is a maximal filter of X.(iii)s is extremal on X.

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Published Online: 2014-11-15
Published in Print: 2014-10-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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