  The paper develops further the theory of quandle rings which was introduced
by the authors in a recent work. Orderability of quandles is defined and many
interesting examples of orderable quandles are given. It is proved that quandle
rings of left or right orderable quandles which are semi-latin have no
zero-divisors. Idempotents in quandle rings of certain interesting quandles are
computed and used to determine sets of maximal quandles in these rings.
Understanding of idempotents is further applied to determine automorphism
groups of these quandle rings. Also, commutator width of quandle rings is
introduced and computed in a few cases. The paper conclude by commenting on
relation of quandle rings with other well-known non-associative algebras.
