title: The left spectrum, the Levitzki radical, and noncommutative schemes.
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.
authors.affiliation: Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.
authors.forename: A L
authors.initials: AL
authors.lastname: Rosenberg