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BY-NC-ND 3.0 license Open Access Published by De Gruyter December 12, 2010

Perfect residuated lattice ordered monoids

  • Jiří Rachůnek EMAIL logo and Dana Šalounová
From the journal Mathematica Slovaca

Abstract

Bounded Rℓ-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 Rℓ-monoids are investigated and it is shown that every good perfect Rℓ-monoid has a state (= an analogue of probability measure).

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Published Online: 2010-12-12
Published in Print: 2010-12-1

© 2010 Mathematical Institute, Slovak Academy of Sciences

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

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