A coordinatisation of nilpotent algebras of prime power order

Description

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.

Period	22 Jun 2018
Event title	First Algebra Week Siena
Event type	Conference
Location	ItalyShow on map