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Classical rings of quotients of semiprime PI-rings. (English. Russian original) Zbl 0799.16018

Algebra Logic 32, No. 1, 1-8 (1993); translation from Algebra Logika 32, No. 1, 3-16 (1993).
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 \(R\)).

MSC:

16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
16U20 Ore rings, multiplicative sets, Ore localization
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References:

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