States on bounded commutative residuated lattices |
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Authors: | Michiro Kondo |
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Institution: | 1. School of Information Environment, Tokyo Denki University, Inzai, 270-1382, Japan
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Abstract: | We define states on bounded commutative residuated lattices and consider their property. We show that, for a bounded commutative residuated lattice X, - If s is a state, then X/ker(s) is an MV-algebra.
- 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: - s is a state-morphism on X.
- ker(s) is a maximal filter of X.
- s is extremal on X.
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