Idempotent discriminators
by
Paolo Agliano
Dipartimento di Matematica, Università di Siena
Coauthors: Kirby A. Baker (UCLA)

A ternary function p on a set is a dual idempotent discriminator if each map c --> p(a, b, c) is the identity function if a =/= b, and is an idempotent function not depending on a if a=b. A variety is a dual idempotent discriminator variety if it has a ternary term that induces a dual idempotent discriminator function on each subdirectly irreducible member. Such varieties are shown to be congruence distributive, semisimple, and in fact filtral. Prominent examples are dual discriminator varieties and dual fixedpoint discriminator varieties. The latter are characterized by being ideal-determined and filtral. Dual idempotent discriminator varieties also have the ternary principal congruence intersection property, which for a finitely generated variety is shown equivalent to being a dual idempotent discriminator variety.

http://www.mat.unisi.it/web/agliano

Date received: June 16, 1999