Dimensions of nilpotent algebras over fields of prime characteristic

Cora M. Stack

Vol. 176 (1996), No. 1, 263–266

DOI: 10.2140/pjm.1996.176.263

Abstract

In this short paper we consider the conjecture that for a finite dimensional commutative nilpotent algebra M over a perfect field of prime characteristic p, dimM ≥ pdimM^(p) where M^p is the subalgebra of M generated by x^p, x ∈ M. We prove that for any finite dimensional nilpotent algebra M (not necessarily commutative) over any field of prime characteristic p, dimM ≥ pdimM^(p) for dimM^(p) ≤ 2.

Mathematical Subject Classification 2000

Primary: 16N40

Milestones

Received: 5 July 1994

Revised: 15 December 1994

Published: 1 November 1996