The left spectrum, the Levitzki radical, and noncommutative schemes.

Rosenberg, A L · Proc Natl Acad Sci U S A · 1990

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Abstract

This note contains a brief exposition of the basics of a noncommutative version of affine, quasi-affine, and projective algebraic geometry. In this version, to any associative ring (with unity) a quasi-affine (resp. affine) left scheme is assigned. The notion of the left spectrum of a ring plays the key role.