Prime Rings with Involution Whose Symmetric Zero-Divisors are Nilpotent

P. M. Cohn
1973 Proceedings of the American Mathematical Society  
Let A: be a field and R the ^-algebra generated by x and j with the single defining relation x"=Q. Using free ring techniques we prove that the set of left zero-divisors of R is Rx. There is a unique involution fixing x, y and this makes R into a prime ring with involution whose symmetric zero-divisors are nilpotent (answering a question by W. S. Martindale). This example also provides us with a subfunctor of the identity whose value is a onesided ideal (answering a question by R. Baer).
doi:10.2307/2038640 fatcat:teku4rn3qbe6rkwfbgfv3g3jaq