Simple periodic rings

William James Rae Mitchell

Vol. 44 (1973), No. 2, 651–658

DOI: 10.2140/pjm.1973.44.651

Abstract

Let A be a power-associative ring, and suppose that for each a ∈ A there exists an integer n = n(a) > 1 such that aⁿ = a. Such a ring A is called a periodic ring. In this paper the structure of all simple periodic rings of characteristic not 2 or 3 is determined. This solves a problem posed by Osborn [Varieties of Algebras, Advances in Mathematics, to appear]. It follows from these results and from Osborn’s that every flexible periodic ring with no elements of additive order 2 or 3 is a Jordan ring.

Mathematical Subject Classification 2000

Primary: 17A05

Milestones

Received: 31 August 1971

Published: 1 February 1973