  In this paper, we study divisorial ideals of a Hibi ring which is a toric
ring arising from a partially ordered set. We especially characterize the
special class of divisorial ideals called conic using the associated partially
ordered set. Using our description of conic divisorial ideals, we also
construct a module giving a non-commutative crepant resolution (= NCCR) of the
Segre product of polynomial rings. Furthermore, applying the operation called
mutation, we give other modules giving NCCRs of it.
