Tomasz Penza – Mal’tsev products of varieties, Part 2

Faculty of Mathematics and Information Science Warsaw University of Technology Koszykowa 75 00-662 Warsaw, Poland
The Mal’tsev product of two varieties need not be a variety itself. In Part 1, a sufficient condition for the Mal'tsev product VoS of some variety V with the variety S equivalent to the variety of semilattices was discussed. In this presentation we generalize that sufficient condition so that we may consider any idempotent variety W instead of just S. We apply this result to Mal'tsev products VoW where V is one of several classical varieties and W is equivalent to some variety of bands (idempotent semigroups). We also present corollaries of the main result that provide other sufficient conditions.