Displaying similar documents to “Measurable Refinement Monoids and Applications to Distributive Semilattices, Heyting Algebras, and Stone Spaces.”

Weak Boolean products of bounded dually residuated l -monoids

Jan Kühr, Jiří Rachůnek (2007)

Mathematica Bohemica

Similarity:

In the paper we deal with weak Boolean products of bounded dually residuated ℓ -monoids (DR l -monoids). Since bounded DRl-monoids are a generalization of pseudo MV-algebras and pseudo BL-algebras, the results can be immediately applied to these algebras.

Direct decompositions of dually residuated lattice-ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.

A duality between algebras of basic logic and bounded representable D R l -monoids

Jiří Rachůnek (2001)

Mathematica Bohemica

Similarity:

B L -algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that B L -algebras are the duals of bounded representable D R l -monoids. This duality enables us to describe some structure properties of B L -algebras.