Rosenberg's classification of maximal clones

Details Rosenberg's classification of maximal clones Rosenberg's classification of maximal clones

2002-11-26

arxiv.org/abs/math/0211420v1

Mathematics

Logic

Diploma Thesis written at the Vienna University of Technology under the guidance of Prof. Martin Goldstern (2002)

Scientific paper

We give a proof of I. G. Rosenberg's characterization of maximal clones. The theorem lists six types of relations on a finite set such that a clone over this set is maximal if and only if it contains just the functions preserving one of the relations of the list. In Universal Algebra, this translates immediately into a characterization of the finite preprimal algebras: A finite algebra is preprimal if and only if its term operations are exactly the functions preserving a relation of one of the six types listed in the theorem. The difficult part of the proof is to show that all maximal clones or preprimal algebras respectively are of that form. This follows from, and, as we also demonstrate, is indeed equivalent to, a characterization of primal algebras: We show that the primal algebras are exactly those whose term operations do not preserve any of the relations on the list.

Affiliated with

Also associated with

No associations

Rating

Rosenberg's classification of maximal clones does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rosenberg's classification of maximal clones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rosenberg's classification of maximal clones will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-140614