👉 In mathematics, a diffident is a type of ring that is a quotient of a principal ideal domain (PID) by a prime ideal. It is also known as a Dedekind domain. A PID is a principal ideal domain in which every ideal is generated by a single element. In a Dedekind domain, the only ideals are zero and the multiplicative identity element. A diffident ring can be defined as a quotient of an integral domain that is not a field (i.e.,