Finite rings and Wilson's theorem

Authors: YASUYUKI HIRANO, MANABU MATSUOKA

Abstract: In this paper we consider the product of all elements in the group of units in a finite ring and we generalize Wilson's theorem to finite rings. As an application, we study some generalizations of Wilson's theorem on residually finite Dedekind domains. And we also give some examples for such rings. Moreover we study some generalizations of Wilson's theorem on rings of matrices over a finite commutative ring.

Keywords: Finite rings, Wilson's theorem, residually finite Dedekind domains

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