A characterization of varieties of inverse semigroups.
A duality between infinitary varieties and algebraic theories
A duality between -ary varieties and -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal , whenever -small products commute with -colimits in , then must be a -filtered category. We nevertheless introduce the concept of -sifted colimits so that morphisms between -ary varieties (defined to be -ary, regular right adjoints) are precisely the functors...
A note on the finite extensivity property
A note on varieties of unary algebras
A sufficient condition for a variety to have the amalgamation property
A ternary variety generated by lattices
Algebraic duality of constant algebras
Algebras with tolerance extension property in 0
An algebraic version of the Cantor-Bernstein-Schröder theorem
The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder theorem for...
Announcements of new results
Classes of graphs definable by graph algebra identities or quasi-identities
Classi e schemi ideali. Congruenze ideali V
Clone compatible identities and clone extensions of algebras
Completely dissociative groupoids
In a groupoid, consider arbitrarily parenthesized expressions on the variables where each appears once and all variables appear in order of their indices. We call these expressions -ary formal products, and denote the set containing all of them by . If are distinct, the statement that and are equal for all values of is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative law holds...
Completion varieties
Complexity of terms, composition, and hypersubstitution.
Conditions de Mal'cev et algèbres universelles uniformes
Conditions for independence of varieties
Congruences and ideals on left divisible involutory groupoids
In [1] ideals and congruences on semiloops were investigated. The aim of this paper is to generalize results obtained for semiloops to the case of left divisible involutory groupoids.
Connected Algebras and Universal Covering