The group of units of some finite local rings I

Abstract

The purpose of this paper is to identify the group of units of finite local rings of the types F2[X]/(Xk) and Z4[X]/I, where I is an ideal. It turns out that they are 2-groups and we give explicit direct sum decomposition into cyclic subgroups of 2-power order and their generators. © 2009 The Korean Mathematical Society.