| Abstract: | Abstract Let R be a prime ring and 𝒰(R) its group of units. We prove that if 𝒰(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 × 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. |
