Algebras with a nilpotent generator over ℤp2

Abstract

The purpose of this paper is to describe the structure of the rings ℤp2 [X])/(α(X)) with α(X) a monic polynomial and X̄k = 0 for some nonnegative integer k. Especially we will see that any ideal of such rings can be generated by at most two elements of the special form and we will find the 'minimal' set of generators of the ideals. We indicate how to identify the isomorphism types of the ideals as ℤp 2-modules by finding the isomorphism types of the ideals of some particular ring. Also we will find the annihilators of the ideals by finding the most 'economical' way of annihilating the generators of the ideal.