On the Representation of Compact Nilpotent Rings by Triangular Matrices

Abstract

We prove that every compact nilpotent ring R of characteristic p > 0 can be embedded in a ring of upper triangular matrices over a compact commutative ring. Furthermore, we prove that every compact topologically nilpotent ring R of characteristic p > 0, is embedded in a ring of infinite triangular matrices over \(\mathbb{F}_{p}^{w(R)}\).