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On the nonexistence of hypercommuting polynomials


Author: Amos Kovacs
Journal: Proc. Amer. Math. Soc. 66 (1977), 241-246
MSC: Primary 16A38; Secondary 13F20
DOI: https://doi.org/10.1090/S0002-9939-1977-0453803-9
MathSciNet review: 0453803
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Abstract: If $ f({x_1}, \ldots ,{x_n})$ is not central for R, then the additive group generated by all specializations of f in R contains a noncentral Lie ideal of R. This is used, among other things, to prove:

Theorem. Let R be a semiprime algebra over an infinite field, $ {f_1}, \ldots ,{f_t}$ polynomials in disjoint sets of variables all noncentral for R. Then, if R satisfies $ {S_t}[{f_1}, \ldots ,{f_t}]$, R must satisfy $ {S_t}[{x_1}, \ldots ,{x_t}]$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0453803-9
Keywords: Extended range, invariant subspace, Lie ideal, polynomial identity, hypercommuting polynomials
Article copyright: © Copyright 1977 American Mathematical Society

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