A Short Contribution to the Classification of the Group of Units of the Rings , and

Lee Xu^1.*, Olalekan Joosati²

¹University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China

²Cape Peninsula University of Technology, South Africa, Faculty of Applied Science

Emails: Leexu1244@yahoo.com; Olalekanjoo1997@cput.ac.za

Abstract

In this paper, we study the group of units problem of three different non-commutative logical extensions rings, where we classify the group of units of the rings , and as semi direct products of well-known abelian groups as the following:

,

,

.

Keywords: Non-commutative logical extension; Group of units; Semi-direct product; Abelian subgroup