Abstract
It is known that a prime ring which satisfies a polynomial identity with derivations applied to the variables must satisfy a generalized polynomial identity, but not necessarily a polynomial identity. In this paper we determine the minimal identity with derivations which can be satisfied by a non-PI prime ringR. The main result shows, essentially, that this identity is the standard identityS 3 withD applied to each variable, whereD = ad(y) fory inR, y 2 = 0, andy of rank one in the central closure ofR.
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Lanski, C. Minimal differential identities in prime rings. Israel J. Math. 56, 231–246 (1986). https://doi.org/10.1007/BF02766126
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DOI: https://doi.org/10.1007/BF02766126