In: Mathematica Slovaca, vol. 64, no. 5
Year, pages: 2014, 1093 - 1104
state, state morphism, residuated lattice, MV-algebra
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 $X$.
How to cite:
Kondo, M. 2014. States on bounded commutative residuated lattices. In Mathematica Slovaca, vol. 64, no.5, pp. 1093-1104. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0261-3
Kondo, M. (2014). States on bounded commutative residuated lattices. Mathematica Slovaca, 64(5), 1093-1104. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0261-3