Pointed Fixedpoint Discriminator Varieties
by
Robert Bignall
The Flinders University of South Australia
Coauthors: Matthew Spinks

Ternary discriminator varieties have been extensively studied and a number of generalisations appear in the literature. We investigate the connections between pointed fixedpoint discriminator varieties and pointed discriminator varieties, that is, ternary discriminator varieties with a constant term.

The variety of implicative BCSK-algebras is a non-commutative generalisation of Abbott's variety of implication algebras, while skew Boolean intersection algebras are a non-commutative analogue of Boolean algebras. The main results of the talk are the following:

1. A pointed variety is a pointed fixedpoint discriminator variety iff it is ideal determined, semisimple with equationally definable principal congruences (EDPC).

2. A variety is a pointed fixedpoint discriminator variety iff it is termwise definitionally equivalent to a variety of implicative BCSK-algebras with compatible operations.

3. A pointed fixedpoint discriminator variety is a discriminator variety iff it is congruence permutable.

4. A variety is a pointed discriminator variety iff it is termwise definitionally equivalent to a variety of skew Boolean intersection algebras with compatible operations.

Date received: September 12, 2003