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GPIs having coefficients in Utumi quotient rings. (English) Zbl 0656.16006
Let \(R\) be a prime ring and \(U\) its Utumi quotient ring. By means of a clever density argument the author proves that \(R\) and \(U\) satisfy the same generalized polynomial identities (GPIs) with coefficients in \(U\), and that if \(R\) satisfies a GPI with coefficients in \(U\), then it satisfies one with coefficients in \(R\). These results generalize those of C. Lanski [Proc. Am. Math. Soc. 98, 17-19 (1986; Zbl 0608.16022)] from the Martindale quotient ring of \(R\) to \(U\), and from multilinear identities to arbitrary ones.
Reviewer: C.Lanski

MSC:
16R50 Other kinds of identities (generalized polynomial, rational, involution)
16P50 Localization and associative Noetherian rings
16N60 Prime and semiprime associative rings
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