Peirce decomposition in simple Lie-admissible power-associative rings

William Eugene Coppage

Vol. 29 (1969), No. 2, 251–258

DOI: 10.2140/pjm.1969.29.251

Abstract

The main result is

Theorem. If A is a simple Lie-admissible power-associative ring with characteristic prime to six, and if A has an idempotent e relative to which A has a Peirce decomposition such that A₀₀ = 0, then either e is a unity element of A or A≅B, where B is a three-dimensional algebra having a basis {e,x,y} such that e² = e, ex = x, ye = y, xy = −yx = e and xe = ey = x² = y² = 0.

Mathematical Subject Classification

Primary: 17.20

Milestones

Received: 21 March 1968

Revised: 17 September 1968

Published: 1 May 1969