Finite local rings

Abstract

In this paper we examine finite local commutative rings which are the building blocks of finite commutative rings. For a finite local ring R our attention centers on the basic structural properties of R, the polynomial ring R[X], the finite local extensions of R and the Galois theory of R. We show that this theory is nearly as complete as that well-known for finite fields. © 1973, Rocky Mountain Mathematics Consortium. All Rights Reserved.