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Displaying 101 – 120 of 152

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 quelques problèmes de plongement en algèbre

C. Henry (1986)

Diagrammes

Sur quelques problèmes de plongements en algèbre

C. Henry (1983)

Diagrammes

Système déterminant de l'algèbre de Morgan libre sur un ensemble ordonné fini

Figallo, Aldo, Monteiro, Luiz (1981)

Portugaliae mathematica

Terms and semiterms

Jaroslav Ježek (1979)

Commentationes Mathematicae Universitatis Carolinae

The class of algebras in which weak independence is equivalent to direct sums independence

Robert M. Vancko (1974)

Colloquium Mathematicae

The free one-generated left distributive algebra: basics and a simplified proof of the division algorithm

Richard Laver, Sheila Miller (2013)

Open Mathematics

The left distributive law is the law a· (b· c) = (a·b) · (a· c). Left distributive algebras have been classically used in the study of knots and braids, and more recently free left distributive algebras have been studied in connection with large cardinal axioms in set theory. We provide a survey of results on the free left distributive algebra on one generator, A, and a new, simplified proof of the existence of a normal form for terms in A. Topics included are: the confluence of A, the linearity...

The ordering of commutative terms

Jaroslav Ježek (2006)

Czechoslovak Mathematical Journal

By a commutative term we mean an element of the free commutative groupoid $F$ of infinite rank. For two commutative terms $a$ , $b$ write $a \leq b$ if $b$ contains a subterm that is a substitution instance of $a$ . With respect to this relation, $F$ is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has...