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Perfect residuated lattice ordered monoids

In: Mathematica Slovaca, vol. 60, no. 6
Jiří Rachůnek - Dana Šalounová
Rok, strany: 2010, 823 - 838
Kľúčové slová:
$R\ell$-monoid, pseudo $BL$-algebra, pseudo $MV$-algebra, local $R\ell$-monoid, perfect $R\ell$-monoid
O článku:
Bounded $R\ell$-monoids form a large subclass of the class of residuated lattices which contains certain of algebras of fuzzy and intuitionistic logics, such as $GMV$-algebras ($=$ pseudo-$MV$-algebras), pseudo-$BL$-algebras and Heyting algebras. Moreover, $GMV$-algebras and pseudo-$BL$-algebras can be recognized as special kinds of pseudo-$MV$-effect algebras and pseudo-weak $MV$-effect algebras, i.e., as algebras of some quantum logics. In the paper, bipartite, local and perfect $R\ell$-monoids are investigated and it is shown that every good perfect $R\ell$-monoid has a state ($=$ an analogue of probability measure).
Ako citovať:
ISO 690:
Rachůnek, J., Šalounová, D. 2010. Perfect residuated lattice ordered monoids. In Mathematica Slovaca, vol. 60, no.6, pp. 823-838. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0050-6

Rachůnek, J., Šalounová, D. (2010). Perfect residuated lattice ordered monoids. Mathematica Slovaca, 60(6), 823-838. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0050-6
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