Abstract
Let R be a ring, M a left R-module. We say that M has Krull dimension, resp. Gabriel dimension, if the lattice L(M) has Krull dimension, resp. Gabriel dimension. The ordinal Kdim L(M), resp. Gdim L(M), will be denoted by Kdim M, resp. Gdim M, and it is called the Krull dimension, resp. Gabriel dimension, of M.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Nǎstǎsescu, C., van Oystaeyen, F. (1987). Krull Dimension and Gabriel Dimension of Rings and Modules. In: Dimensions of Ring Theory. Mathematics and Its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3835-9_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-3835-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8207-5
Online ISBN: 978-94-009-3835-9
eBook Packages: Springer Book Archive