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Super-De Morgan functions and free De Morgan quasilattices

Yuri Movsisyan, Vahagn Aslanyan (2014)

Open Mathematics

A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....

Sur les treillis de Coxeter finis

C. Le Conte de Poly-Barbut (1994)

Mathématiques et Sciences Humaines

Björner (1984) a montré que l’ordre faible de Bruhat défini sur un groupe de Coxeter fini (Bourbaki 1969) est un treillis. Dans le cas du groupe symétrique S n ce résultat (treillis permutoèdre) a été prouvé par Guilbaud-Rosenstiehl (1963). Dans ce papier nous montrons que des propriétés connues des treillis permutoèdres peuvent s’étendre à tous les treillis de Coxeter finis et qu’inversement des propriétés démontrées sur tous les Coxeter finis ont des retombées intéressantes sur les permutoèdres....

The clean elements of the ring ( L )

Ali Akbar Estaji, Maryam Taha (2024)

Czechoslovak Mathematical Journal

We characterize clean elements of ( L ) and show that α ( L ) is clean if and only if there exists a clopen sublocale U in L such that 𝔠 L ( coz ( α - 1 ) ) U 𝔬 L ( coz ( α ) ) . Also, we prove that ( L ) is clean if and only if ( L ) has a clean prime ideal. Then, according to the results about ( L ) , we immediately get results about 𝒞 c ( L ) .

The completely distributive lattice of machine invariant sets of infinite words

Aleksandrs Belovs, Jānis Buls (2007)

Discussiones Mathematicae - General Algebra and Applications

We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.

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