Rings on Torsion-Free Groups of Rank One and Two

Abstract

This paper gives a survey about the possible rings which may be defined over torsion-free groups of rank one and two. In fact, we give a list of such rings which have been studied by some mathematicians over the past decades. In particular, we give a review of the authors' studies to determine such rings.

Key words and phrases. ring, rank, type.

2000 Mathematics Subject Classification. 20K15, 20K27