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On the classical Krull dimension of rings. (English) Zbl 0542.16022

For a ring R the author considers the classical Krull dimension as introduced by the reviewer [Math. Z. 118, 207-214 (1970; Zbl 0194.066)] and the derived dimension resulting from certain topologies on spec(R). He proves that R has classical Krull dimension if and only if spec(R) has derived dimension, and that, when defined, the two dimensions differ by at most one.
Reviewer: G.Krause

MSC:

16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16Dxx Modules, bimodules and ideals in associative algebras
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