A commutativity theorem for non-associative algebras over a principal ideal domain

Jiang Luh and Mohan S. Putcha

Vol. 68 (1977), No. 2, 485–488

DOI: 10.2140/pjm.1977.68.485

Abstract

Let A be an algebra (not necessarily associative) over a principal ideal domain R such that for all a,b ∈ A, there exist α,β ∈ R such that (α,β) = 1 and αab = βba. It is shown that A is commutative.

Mathematical Subject Classification 2000

Primary: 17A30

Milestones

Received: 5 October 1976

Published: 1 February 1977