NILPOTENT ELEMENTS AND IDEALS IN ALTERNATIVE LOOP RINGS

Abstract

We show that if the torsion subloop of an RA loop L is central, then there exist no nonzero nilpotent elements in the loop algebra over any commutative ring, with some obvious exceptions. We also study the nilpotency of augmentation ideals and prove that integral loop rings contain no nontrivial idempotent ideals