The nil radical of power series rings |
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| Authors: | E. R. Puczyłowski Agata Smoktunowicz |
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| Affiliation: | (1) Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland;(2) Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warsaw, Poland |
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| Abstract: | We describe the nil radical of power series rings in non-commuting indeterminates by showing that a series belongs to the radical if and only if the ideal generated by its coefficients is nilpotent. We also show thatt the principal ideals generated by elements of the nil radical of the power series ring in one indeterminate are nil of bounded index. |
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