Prime rings with involution whose symmetric zero-divisors are nilpotent
Abstract: Let be a field and the -algebra generated by and with the single defining relation . Using free ring techniques we prove that the set of left zero-divisors of is . There is a unique involution fixing and this makes 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).
Keywords: Prime ring, involution, zero-divisor, nilpotent, free ring, weak algorithm
Article copyright: © Copyright 1973 American Mathematical Society