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Eingeladener Vortrag an Universität

Describing polynomial functions of universal algebras

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Zusammenfassung: From results of Fr\"ohlich, Maurer, and Rhodes we know that every function on a finite simple non-abelian group is a polynomial function; these groups are called *polynomially complete*. Later, it was studied when every congruence preserving function on an algebra is a polynomial function; such algebras were called *affine complete*. We will start from the following questions: 1. Is there an algorithm that decides whether a given finite algebra is affine complete? 2. Can the polynomial functions of a finite algebra be described as those that preserve a certain finite set of relations? 3. We call two finite algebras polynomially equivalent if they have the same set of polynomial functions. How many nonequivalent finite algebras do exist? And how many of those have a Malcev term? We cannot answer any of these questions completely, but we will present several new results (by Juergen Ecker, Peter Mayr, Nebojsa Mudrinski, and the speaker) that are motivated by these questions.

Vortragsdatum: 20.10.2006
Web: http://www.dmg.tuwien.ac.at/fg1/seminar.html (Wiener Algebra Seminar (WAS))
Land: Österreich
Ort: Technische Universitaet Wien Wien

Beteiligte

ReferentInnen: Assoz.Univprof. DI Dr. Erhard Aichinger

Forschungseinheiten der JKU:

Wissenschaftszweige: 101 Mathematik | 101001 Algebra | 101005 Computeralgebra | 101013 Mathematische Logik | 102031 Theoretische Informatik

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