A reference book for Schur's lemma We want to find the reference book for some version of the Schur's lemma which covers the following result
Let $A$ be an assoiative algebra over $\mathbb{C}$ with countable basis, then any central element acts on any simple $A$-module as a scalar.
Thanks
 A: This is (an immediate consequence of) Lemma 2.1.3(b) in Chriss-Ginzburg.
A: Doc, if you want to be anal with your references, you should quote
Amitsur, A. S. Algebras over infinite fields. Proc. Amer. Math. Soc. 7 (1956), 35–48.
Otherwise, this is a well-known fact and you can just refer to it as "Amitsur's Trick" or "Noncommutative Nullstellensatz". Chapter 9 of McConnell-Robson-Noncommutative-Noetherian-Rings is devoted entirely to this property and its finer variations.
A: From Wikipedia:


*

*David S. Dummit, Richard M. Foote. Abstract Algebra. 2nd ed., pg. 337.

*Lam, Tsit-Yuen (2001), A First Course in Noncommutative Rings, Berlin, New York: Springer-Verlag, ISBN 978-0-387-95325-0


From Google Books:


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*William Fulton, Joe Harris. Representation Theory.

*William Arveson. An Invitation to C*-Algebras.


I hope that helps you a bit.
P.s: I wanted to post this in a comment, but the comment button isn't available for some reason.
A: This is also in Bourbaki's Algebra 8 (most recent edition), Section 3, number 2, Example, page 43.  This reference is online if you have access to SpringerLink.
