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Invariant dimension and restricted extension of Noetherian rings

  • Walter Borho
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 924)

Abstract

This paper is an alternative and complement to [1]. First we take up the idea of an axiomatic notion of dimension generalizing and unifying Gelfand-Kirillov- and Gabriel-Rentschler-dimension. We introduce an “axiom of invariance”, generalizing an idea of Stafford. Next we apply this to reprove the main results of [1] on “good behaviour” of prime ideals in certain extension-rings of noncommutative rings, including an additivity principle for Goldie-ranks. Finally we discuss the extent to which our “restriction” on extensions is also necessary in order to have results of this type.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Walter Borho
    • 1
  1. 1.FB 7-MathematikWuppertal 1Germany

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