Noncrossed product division algebras with a Baer ordering

Abstract

Let n | m n|m be positive integers with the same prime factors, such that p 3 | n {p^3}|n for some prime p. We construct a noncrossed product division algebra D with involution ∗ \ast , of index m and exponent n, such that D possesses a Baer ordering relative to the involution ∗ \ast . Using similar techniques we construct indecomposable division algebras with involution possessing a Baer ordering.