We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely -based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely -based.
Let be a group, and be a semi-Hopf -algebra. We first show that the category of left -modules over is a monoidal category with a suitably defined tensor product and each element in induces a strict monoidal functor from to itself. Then we introduce the concept of quasitriangular semi-Hopf -algebra, and show that a semi-Hopf -algebra is quasitriangular if and only if the category is a braided monoidal category and is a strict braided monoidal functor for any . Finally,...
Two properties of the lattice of quasivarieties of pseudocomplemented semilattices are established, namely, in the quasivariety generated by the 3-element chain, there is a sublattice freely generated by ω elements and there are quasivarieties.
For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.