Algebra pp 117-172 | Cite as

Modules

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 211)

Abstract

Although this chapter is logically self-contained and prepares for future topics, in practice readers will have had some acquaintance with vector spaces over a field. We generalize this notion here to modules over rings. It is a standard fact (to be reproved) that a vector space has a basis, but for modules this is not always the case. Sometimes they do; most often they do not. We shall look into cases where they do.

Keywords

Filtration Prefix Verse Veri 

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References

  1. [CCFT.
    91]_P. Cassou-Nogues, T. Chinburg, A. Frohlich, M. J. Taylor, L-functions and Galois modules, in L-functions and Arithmetic J. Coates and M.J. Taylor (eds.), Proceedings of the Durham Symposium July 1989, London Math, Soc. Lecture Note Series 153, Cambridge University Press (1991), pp. 75–139Google Scholar
  2. [La 82]
    S. Lang, Units and class groups in number theory and algebraic geometry, Bull. AMS Vol. 6 No. 3 (1982), pp. 253–316MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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