Group Identities and Prime Rings Generated by Units

Abstract

Let R be a prime ring and U(R) the group of units of R. We prove that if U(R) generates R and satisfies a group identity,then R is either a domain or a full matrix ring over a finite field.

Key Words:

• Group identities
• Units
• Prime rings
• Generalized polynomial identities

2000 Mathematics Subject Classification:

• 16U60
• 16N60

Acknowledgments

The work was partially supported by NSC. The second author thanks National Sun Yat-sen University. Part of the research was done there.