Generalized Quaternion Rings over Z/nZ for an Odd n

摘要

We consider a generalization of the quaternion ring (a,b/R) over a commutative unital ring R that includes the case when a and b are not units of R. In this paper, we focus on the case R = Z/nZ for and odd n. In particular, for every odd integer n we compute the number of non R-isomorphic generalized quaternion rings (a,b/Z/nZ ).