Derivations with Invertible or Nilpotent Values on a Multilinear Polynomial
Resource
Algebra Colloquium 7 (1): 93-98
Journal
Algebra Colloquium
Pages
93-98
Date Issued
2000
Date
2000
Author(s)
Lee, P.-H
Wong, T.L.
Abstract
Let R be a prime ring with no non-zero nil one-sided ideals, d a nonzero derivation on R, and f(X1,...,X t ) a multilinear polynomial not central-valued on R. Suppose d(f(x1,...,x t )) is either invertible or nilpotent for all x1,...,x t in some non-zero ideal of R. Then it is proved that R is either a division ring or the ring of 2 × 2 matrices over a division ring. This theorem is a simultaneous generalization of a number of results proved earlier.
Type
journal article
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