Algebra and Logic Seminar

The next meeting of the seminar will be held on May 20, 2016 (Friday), at 11:00, in Room 578 of the Institute of Mathematics and Informatics.

A talk on

Semigroups of sets of n-ary Boolean operations

will be delivered by Prof. Jörg KOPPITZ^*) (Institut für Mathematik der Universität Potsdam, Germany).

Everybody is invited.

Abstract. Any n-ary Boolean operation can be regarded as a transformation on the set of n-tuples, where the image is in a two-element set. Hence, the set of all n-ary Boolean operations corresponds to a set of transformations. Under the composition of transformations, this set forms a semigroup which is called transformation semigroup with restricted range. On the other hand, one can define an associative binary operation on the set of all n-ary Boolean operations based on the composition operator. This provides again a semigroup being isomorphic to a semigroup with restricted range, which is already well studied. It is well known that the complex product is an associative operation on power set of the transformations with restricted range. In this presentation, we will discuss this semigroup. In particular, we determine their idempotent and regular elements. Further, we characterize the (maximal) regular subsemigroups, the largest semiband, and the (maximal) idempotent subsemigroups.

*) Supported by Humbodt-Foundation.