Derivations of polynomial identity rings

Question

Does anyone have any references to general theory of derivations of PI rings? I have had a quick look around without much luck.

Answer 1

I am not sure if this should count as an answer, but derivations make an appearance in the following books on PI Algebras:

1. Computational Aspects of Polynomial Identities by Alexei Kanel-Belov, Yakov Karasik, Louis Halle Rowen
2. Polynomial Identities And Combinatorial Methods by Antonio Giambruno, Amitai Regev, Mikhail Zaicev
3. Polynomial Identity Rings by Vesselin Drensky, Edward Formanek
4. Razmyslov, Yu. P. Identities of algebras and their representations. Translated from the 1989 Russian original by A. M. Shtern. Translations of Mathematical Monographs, 138. American Mathematical Society, Providence, RI, 1994. xiv+318 pp. ISBN: 0-8218-4608-6
5. Beidar, K. I.; Martindale, W. S., III; Mikhalev, A. V. Rings with generalized identities. Monographs and Textbooks in Pure and Applied Mathematics, 196. Marcel Dekker, Inc., New York, 1996. xiv+522 pp. ISBN: 0-8247-9325-0

I don't know of any books dedicated to derivations of PI algebras however. For what it is worth, I am a particular fan of the book by Drensky and Formanek (although there is not much about derivations in that book except their use in proving Kuzmin's lower bound on the class of nilpotency). On the other hand, according to the MathSciNet reviews I read there are entire chapters devoted to derivations in the books (4) and (5) listed above.

Also, a quick search on MathSciNet using the key words "PI Algebra" and "Derivation" led to a bunch of papers (in addition to books). Here is one whose title stood out to me given your interests:

Van Oystaeyen, F.; Verschoren, A. Derivations of PI-algebras and smoothness of noncommutative curves. J. Pure Appl. Algebra 29 (1983), no. 2, 169–176.