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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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##### References:
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