Some properties of finite rings

Rodney Coleman (1)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques

A well-known theorem of Wedderburn asserts that a finite division ring is commutative. In a division ring the group of invertible elements is as large as possible. Here we will be particularly interested in the case where this group is as small as possible, namely reduced to 1. We will show that, if this is the case, then the ring is boolean. Thus, here too, the ring is commutative.

Mots clés: Finite ring; group of invertible elements.; group of invertible elements

Domaines: Anneaux et algèbres [math.RA]

Rodney Coleman. Some properties of finite rings. 2013. ⟨hal-00788113⟩