Chuang, Chen-Lian GPIs having coefficients in Utumi quotient rings. (English) Zbl 0656.16006 Proc. Am. Math. Soc. 103, No. 3, 723-728 (1988). 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 Cited in 1 ReviewCited in 274 Documents MSC: 16R50 Other kinds of identities (generalized polynomial, rational, involution) 16P50 Localization and associative Noetherian rings 16N60 Prime and semiprime associative rings Keywords:prime rings; Utumi quotient rings; generalized polynomial identities; multilinear identities Citations:Zbl 0608.16022 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] S. A. Amitsur, Generalized polynomial identities and pivotal monomials, Trans. Amer. Math. Soc. 114 (1965), 210 – 226. · Zbl 0131.03202 [2] Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. · Zbl 0162.05002 [3] Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. · Zbl 0053.21204 [4] Nathan Jacobson, \?\?-algebras, Lecture Notes in Mathematics, Vol. 441, Springer-Verlag, Berlin-New York, 1975. An introduction. · Zbl 0314.15001 [5] V. K. Harčenko, Differential identities of prime rings, Algebra i Logika 17 (1978), no. 2, 220 – 238, 242 – 243 (Russian). [6] Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. · Zbl 0365.16001 [7] Charles Lanski, A note on GPIs and their coefficients, Proc. Amer. Math. Soc. 98 (1986), no. 1, 17 – 19. · Zbl 0608.16022 [8] Wallace S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576 – 584. · Zbl 0175.03102 · doi:10.1016/0021-8693(69)90029-5 [9] Neal H. McCoy, The theory of rings, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1964. · Zbl 0273.16001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.