Idealizer Rings and Noncommutative Projective Geometry

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We study some properties of graded idealizer rings with an emphasis on applications to the theory of noncommutative projective geometry. In particular we give examples of rings for which the $χ$-conditions of Artin and Zhang and the strong noetherian property have very different behavior on the left and right sides.
17 Pages, revised version: significant changes--introduction rewritten, new section on tensor products added, main theorem restated at end

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