Skip to main content

Ext and Tor

  • Chapter
  • 9570 Accesses

Part of the Graduate Texts in Mathematics book series (GTM,volume 242)

Homological algebra, the study of homology groups and related constructions, was a branch of algebraic topology until Eilenberg and MacLane [1942] devised a purely algebraic cohomology of groups, which shared many features with the cohomology of topological spaces. Recognition as a separate branch of algebra came with the book Homological Algebra [1956], by Cartan and Eilenberg. This chapter contains the basic properties of homology groups, resolutions, Ext, and Tor, with applications to groups and rings. As before, all rings have an identity element, and all modules are unital.

Keywords

  • Abelian Group
  • Exact Sequence
  • Commutative Diagram
  • Short Exact Sequence
  • Natural Isomorphism

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-0-387-71568-1_12
  • Chapter length: 52 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-71568-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.95
Price excludes VAT (USA)
Hardcover Book
USD   69.95
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

(2007). Ext and Tor. In: Abstract Algebra. Graduate Texts in Mathematics, vol 242. Springer, New York, NY. https://doi.org/10.1007/978-0-387-71568-1_12

Download citation