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Direct decompositions of dually residuated lattice-ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Discussiones Mathematicae - General Algebra and Applications

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.

Direct product decompositions of bounded commutative residuated ℓ -monoids

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

The notion of bounded commutative residuated ℓ -monoid ( B C R ℓ -monoid, in short) generalizes both the notions of M V -algebra and of B L -algebra. Let A ̧ be a B C R ℓ -monoid; we denote by ℓ ( A ̧ ) the underlying lattice of A ̧ . In the present paper we show that each direct...

Discussion of the structure of uninorms

Paweł Drygaś (2005)

Kybernetika

The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sum are depending on the set of values of a decreasing...

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

This paper deals with implications defined from disjunctive uninorms U by the expression I ( x , y ) = U ( N ( x ) , y ) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t -norm or a t -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications...

Every braid admits a short sigma-definite expression

Jean Fromentin (2011)

Journal of the European Mathematical Society

A result by Dehornoy (1992) says that every nontrivial braid admits a σ -definite expression, defined as a braid word in which the generator σ i with maximal index i appears with exponents that are all positive, or all negative. This is the ground result for ordering braids. In this paper, we enhance this result and prove that every braid admits a σ -definite word expression that, in addition, is quasi-geodesic. This establishes a longstanding conjecture. Our proof uses the dual braid monoid and a new...

Extensions of partially ordered partial abelian monoids

Sylvia Pulmannová (2006)

Czechoslovak Mathematical Journal

The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.

Currently displaying 81 – 100 of 366