Abstract
Let R be a nil ring with p R = 0 for some prime number p. We show that the polynomial ring R[x,y] in two commuting indeterminates x, y over R cannot be homomorphically mapped onto a ring with identity. This extends, in finite characteristic case, a result obtained by Smoktunowicz [8] and gives a new approximation, in that case, of a positive solution of Köthe’s problem.
Acknowledgment: The fourth author was supported by KBN Grant No. 1 P03A 032 27. This work was finished when he was a visiting scholar at the National Center for Theoretical Sciences, Taipei Office, Taiwan.
To Robert Wisbauer
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Chebotar, M.A., Ke, W.F., Lee, P.H., Puczyłowski, E.R. (2008). A Note on Polynomial Rings over Nil Rings. In: Brzeziński, T., Gómez Pardo, J.L., Shestakov, I., Smith, P.F. (eds) Modules and Comodules. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8742-6_10
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DOI: https://doi.org/10.1007/978-3-7643-8742-6_10
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