Classical rings of quotients of semiprime PI-rings
The author considers the problem, when a semiprime P. I. ring has a classical quotient ring. Examples of Bergman and Markov show that there exist semiprime P. I. rings without classical quotient rings. The main result of the paper under review is that a semiprime P. I. ring \(R\), which is right p. p. and with an upper bound \(n\) of nilpotency index of elements of \(R\) has a classical quotient ring, \(Q_{cl}(R)\). Moreover, \(Q_{cl}(R)\) is strongly right \(n\) regular P. I. and \(n\)-regular p. p., \(P \to P \cap R\) gives a bijection between \(\text{Max Spec }Q_{cl}(R)\) and \(\text{Min Spec}(R)\). A major tool in the proof is a study of the ring \(Q_ e(R)\) generated by \(R\) and the Boolean ring of central idempotents of \(Q(R)\), (the maximal quotient ring of \(R\)).
scientific article; zbMATH DE number 536684