Eggert’s conjecture on the dimensions of nilpotent algebras

Lakhdar Hammoudi

Vol. 202 (2002), No. 1, 93–97

DOI: 10.2140/pjm.2002.202.93

Abstract

In this paper we prove that for a finite dimensional commutative nilpotent algebra A over a field of prime characteristic p > 0, dimA ≥ p dimA^(p), where A^(p) is the subalgebra of A generated by the elements x^p. In particular, this solves Eggert’s conjecture.

Milestones

Received: 30 July 1998

Revised: 19 April 2000

Published: 1 January 2002

Correction: 1 January 2005