Invariant dimension and restricted extension of Noetherian rings
This paper is an alternative and complement to . 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  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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