Certain algebras of degree one

Frank James Kosier

Vol. 15 (1965), No. 2, 541–544

DOI: 10.2140/pjm.1965.15.541

Abstract

In this note the following is proved: Suppose R is a finite-dimensional algebra over an algebraically closed field F of characteristic 0 whose associator satisfies 4(y,x,x) = 4(x,y,x) + [[y,x],x] and (x,x,x) = 0. If R is simple and non-nil then R is iso-morphic to F.

Mathematical Subject Classification

Primary: 17.10

Milestones

Received: 6 April 1964

Published: 1 June 1965