Embedding rings with a maximal cone and rings with an involution in quaternion algebras

A note on embedding a partially ordered ring in a division algebra

“…We will show that with stronger hypotheses, the conic hemiring of Theorems 1,2, and 3 in [3] can be replaced by a maximal cone to obtain Theorems 1, 2, and 3 listed below. This is of interest since, as observed in [2], maximal cones are somewhat more plentiful than conic hemirings. Our first theorem is of a more general nature.…”

“…[January (2) If in addition to the hypothesis of (I), H is commutative, then H' is left central in A' and A' is a division ring.…”