Skip to main content

Krull Dimension and Gabriel Dimension of Rings and Modules

  • Chapter
Dimensions of Ring Theory

Part of the book series: Mathematics and Its Applications ((MAIA,volume 36))

  • 320 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Publish with us

Policies and ethics