#### Z. Reichstein, N. Vonessen *
Polynomial identity rings as rings of functions,
* Journal of Algebra, 310, Issue 2 (2007), 624--647.

** Abstract: **
We generalize the usual relationship between irreducible Zariski
closed subsets of the affine space, their defining ideals,
coordinate rings, and function fields, to a non-commutative setting,
where ``varieties" carry a PGL_n action, regular and rational
``functions" on them are matrix-valued, ``coordinate rings" are
prime polynomial identity algebras, and ``function fields" are
central simple algebras of degree n. In particular, a prime
polynomial identity algebra of degree n is finitely generated if
and only if it arises as the ``coordinate ring" of a ``variety'' in this
setting. For n = 1 our definitions and results reduce to those of
classical affine algebraic geometry.

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