A characterization of semilattices of left or right groups
A characterization of Sheffer functions by hyperidentities.
A characterization of the arc by means of the C-index of itssemigroup.
A characterization of the group congruences on a semigroup.
A characterization of varieties of inverse semigroups.
A class of commutative semigroups in which the idempotents are linearly ordered
A class of maximal inverse subsemigroups of TX.
A class of quasi-adequate transformation semigroups.
A class of rectangular bands of inverse semigroups.
A class of regular *-semigroups.
A class of semigroups embeddable in groups.
A class of semigroups having almost trivial multiplications.
A class of uniform bands.
A classification of rational languages by semilattice-ordered monoids
We prove here an Eilenberg type theorem: the so-called conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilattice-ordered monoids. Taking complements of members of a conjunctive variety of languages we get a so-called disjunctive variety. We present here a non-trivial example of such a variety together with an equational characterization of the corresponding pseudovariety.
A combinatorial theorem on -power-free words and an application to semigroups
A common generalization of Kelley's theorem (concerning measures on Boolean algebra) and on von Neumann's minimax theorem
A comparison of some generalizations of Green's relations.
A completion theorem for finitely generated commutative semigroups.
A concept of variety for regular biordered sets.
A conjecture on the concatenation product
In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal’cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case. Another...