Prime rings whose units satisfy a group identity. II

摘要

Let R be a prime ring and U(R) its group of units. We prove that if W(R) satisfies a group identity and U(R) generates R, then either R is a domain or R is isomorphic to the algebra of n x n matrices over a finite field of order d. Moreover the integers n and d depend only on the group identity satisfed by U(R). This result has been recently proved by C. H. Liu and T. K. Lee (Liu, C. H.; Lee, T. K. Group identities and prime rings generated by units. Comm. Algebra (to appear)) and here we present a new different proof. References: 7