The affine scheme associated to a nonnoetherian prime pi algebra

Springer Science and Business Media LLC - Tập 53 - Trang 121-128 - 1986
A. Verschoren1
1Department of Mathematics, University of Antwerp, U.I.A., Wilrijk, Belgium

Tóm tắt

It is shown how abstract localization theory may be applied in order to associate to a not necessarily noetherian pi algebra a ringed space (Spec(R),O R), which behaves functorially with respect to extensions and which possesses suitable features allowing one to study this type of ring from a geometric point of view. These results generalize previous ones, obtained by F. Van Oystaeyen and the author in the noetherian case.

Tài liệu tham khảo

M. Artin,On Azumaya algebras and finite dimensional representations of rings, J. Algebra11 (1969), 532–563. A. Braun,The radical of a finitely generated P.I.-algebra, Bull. Am. Math. Soc.7 (1982), 385–386. J. P. Delale,Sur le spectre d’un anneau noncommutatif, thèse, Univ. de Paris — Sud, Centre d’Orsay, 1974. R. Godement,Theorie des faisceaux, Hermann, Paris, 1958. S. J. Golan,Localization of Noncommutative Rings, M. Dekker, New York, 1973. O. Goldman,Rings and modules of quotients, J. Algebra13 (1969), 10–47. B. Mueller,The quotient category of a Morita context, J. Algebra28 (1974), 389–407. D. Murdoch and F. Van Oystaeyen,Noncommutative localization and sheaves, J. Algebra35 (1975), 500–515. C. Procesi,Rings with Polynomial Identities, M. Dekker, New York, 1973. B. Stenstrom,Rings of Quotients, Springer-Verlag, Berlin, 1975. F. Van Oystaeyen,Prime Spectra in Noncommutative Algebra, Lecture Notes in Math.444, Springer-Verlag, Berlin, 1975. F. Van Oystaeyen and A. Verschoren,Relative localization, bimodules and semiprime P.I. Rings, Comm. Algebra7 (1979), 955–988. F. Van Oystaeyen and A. Verschoren,Noncommutative Algebraic Geometry, Lecture Notes in Math.887, Springer-Verlag, Berlin, 1981.