On the congruences of algebras defined on sectionally pseudocomplemented (not necessarily distributive) lattices
by
Sándor Radeleczki
Mathematical Institute, University of Miskolc
Coauthors: Ivan Chajda, Department of algebra and geometry, Palacky University Olomouc

Lattices with 1, where for each element a of L the interval [a, 1] is pseudocomplemented, can be equiped with a binary operation ° similar to the operation of relative pseudocomplementation. Although lattices with relative pseudocomplementation are always distributive, this operation ° can be defined for nondistributive lattices, for instance for finite sublattices of free lattices. These algebras (defined by adding ° to the lattice operations) form an arithmetical and 1-regular variety. We investigate the subvarieties and the congruence kernels in this variety. We prove that the congruences of a such a finite algebra are induced by special dually distributive elements of L. If L is a finite sublattice of a free lattice, then the congruences of the corresponding algebra have in addition some remarkable properties. (Joint work with Ivan Chajda.)

Date received: February 24, 2003