Refinement Monoids, Vaught Monoids, and Boolean Algebras.
Hans Dobbertin (1983)
Mathematische Annalen
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Hans Dobbertin (1983)
Mathematische Annalen
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W. Taylor, J. Hyndman, R. McKenzie (1992)
Semigroup forum
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Zdenek Hedrlin, Pavel Goralcik (1971)
Mathematische Zeitschrift
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Л.А. Скорняков (1985)
Matematiceskij sbornik
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Jan Kühr, Jiří Rachůnek (2007)
Mathematica Bohemica
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In the paper we deal with weak Boolean products of bounded dually residuated -monoids (DR-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.
Jiří Rachůnek, Dana Šalounová (2004)
Discussiones Mathematicae - General Algebra and Applications
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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.
S. Margolis, J.E. Pin (1984)
Semigroup forum
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P. Normak (1992)
Semigroup forum
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A.V. Mikhalev, U. Knauer (1974)
Semigroup forum
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Jiří Rachůnek (2001)
Mathematica Bohemica
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-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that -algebras are the duals of bounded representable -monoids. This duality enables us to describe some structure properties of -algebras.