#### Z. Reichstein,
D. Rogalski , J. J. Zhang, * Projectively simple rings
*, Advances in Math. 203, Issue 2, Pages 365-407

**Abstract:**
We introduce the notion of a projectively simple ring, which is an
infinite-dimensional graded k-algebra A such that every
2-sided ideal has finite codimension in A (over the base field k).
Under some (relatively mild) additional assumptions on A, we reduce
the problem of classifying such rings (in the sense
explained in the paper) to the following purely geometric
question, which we believe to be of independent interest.

Let X is a smooth irreducible projective variety. An automorphism f: X -> X
is called * wild * if it X has no proper f-invariant subvarieties.
We conjecture that if X admits a wild automorphism then
X is an abelian variety. We prove several results
in support of this conjecture; in particular, we show that
the conjecture is true if X is a curve or a surface. In
the case where X is an abelian variety, we describe all
wild automorphisms of X.

In the last two sections we show that if A is projectively
simple and admits a balanced dualizing complex,
then Proj(A) is Cohen-Macaulay and Gorenstein.

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