GPIs having coefficients in Utumi quotient rings
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- by Chen-Lian Chuang
- Proc. Amer. Math. Soc. 103 (1988), 723-728
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947646-4
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Abstract:
Let $R$ be a prime ring and let $U$ be its Utumi quotient ring. We prove the following: (1) If $R$ satisfies a GPI having all its coefficients in $U$, then $R$ satisfies a GPI having all its coefficients in $R$. (2) $R$ and $U$ satisfy the same GPIs having their coefficients in $U$.References
- S. A. Amitsur, Generalized polynomial identities and pivotal monomials, Trans. Amer. Math. Soc. 114 (1965), 210–226. MR 172902, DOI 10.1090/S0002-9947-1965-0172902-9
- Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206
- Nathan Jacobson, Lectures in abstract algebra. Vol. II. Linear algebra, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0053905
- Nathan Jacobson, $\textrm {PI}$-algebras, Lecture Notes in Mathematics, Vol. 441, Springer-Verlag, Berlin-New York, 1975. An introduction. MR 0369421
- V. K. Harčenko, Differential identities of prime rings, Algebra i Logika 17 (1978), no. 2, 220–238, 242–243 (Russian). MR 541758
- Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
- Charles Lanski, A note on GPIs and their coefficients, Proc. Amer. Math. Soc. 98 (1986), no. 1, 17–19. MR 848865, DOI 10.1090/S0002-9939-1986-0848865-6
- Wallace S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. MR 238897, DOI 10.1016/0021-8693(69)90029-5
- Neal H. McCoy, The theory of rings, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0188241
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 723-728
- MSC: Primary 16A38; Secondary 16A08, 16A12
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947646-4
- MathSciNet review: 947646