A coordinatisation of nilpotent algebras of prime power order
Sprache des Vortragstitels:
Deutsch
Original Tagungtitel:
First Algebra Week Siena
Sprache des Tagungstitel:
Deutsch
Original Kurzfassung:
Abstract. A fundamental theorem on nilpotency (proved by
Vaughan-Lee, Freese, McKenzie, Berman, and Blok) states that ev-
ery nilpotent algebra in a congruence modular variety with finitely
many fundamental operations is supernilpotent, i.e., has a ?small
free spectrum?. We re-prove this result by using a coordinatisation
of the algebra by polynomials over a finite field, and thereby obtain
a bound on the supernilpotency degree of such an algebra. For this
purpose, we study some possible definitions of supernilpotency, the
interaction of the basic operations of an algebra with the binary
modular commutator, a coordinatisation of nilpotent algebras of
prime power order with finite fields, and a representation of clones
by polynomials over this field.
Sprache der Kurzfassung:
Englisch
Vortragstyp:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung
Forschungs-