Quotients induced from exponents of finite commutative rings

Abstract

We use the concept of exponent of finite commutative rings to define the Carmichael quotients and the Carmichael quotients of degree d over polynomial rings over finite local rings, and then we give some congruence relations of these quotients. Moreover, we define the Carmichael quotients and the Wilson quotients over the ring of integers of number fields and study some congruence relations between them.