On the problem of basis for solid quasivarieties
by
Ewa Graczyńska
Institute of Mathematics, Tehnical University of Opole, Poland

The aim of my talk is to present an answer to the Problem Nr 31 of Chapter 8 of the monograph of K. Denecke and S. L. Wismath [1] by the following: THEOREM: Given a quasivariety QV defined by a set B of quasi-identities. These quasi-identities are satisfied in QV as hyper-quasi-identities if and only if QV is solid (is a hyperquasivariety).

Moreover, each quasi-identity satisfied in a solid quasivariety QV is satisfied in QV as a hyper-quasi-identity and vice versa.

By other words, we observed that solid quasivarieties are always defined by a hyperbasis.

A suitable modification of the above theorem will be presented for so called M-hyper-quasi-identities, for a given monoid M of hypersubstitutions.

References [1] K. Denecke, S. L. Wismath, Hyperidentities and clones, Algebra, Logic and Applications Series Volume 14, Gordon and Breach Science Publishers 2000. ISBN 90-5699-235-X, ISSN 1041-5394.

Date received: May 10, 2004