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Algebra pp 498-519 | Cite as

Quotient Categories and Localizing Functors

  • Carl Faith
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 190)

Abstract

Let A be an abelian category. A Serre class or subcategory of A is a nonempty full subcategory S such that for every exact sequence
$$0 \to A \to B \to C \to 0 $$
in A it is true that
$$B \in \mathcal{S} \Leftrightarrow A \in \mathcal{S}\& C \in \mathcal{S}.$$

Keywords

Full Subcategory Abelian Category Torsion Theory Canonical Morphism Exact Functor 
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.

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References

  1. [68]
    Amitsur, S. A.: Rings with involution. Israel J. Math. 6, 99–106 (1968).zbMATHMathSciNetGoogle Scholar
  2. [62]
    Cohn, P. M.: On subsemigroups of free semigroups. Proc. Amer. Math. Soc. 13, 347–351 (1962).CrossRefzbMATHMathSciNetGoogle Scholar
  3. [64]
    Faith, C.: Noetherian simple rings. Bull. Amer. Math. Soc. 70, 730— 731 (1964).Google Scholar
  4. [71]
    Fuller, K. R.: Primary rings and double centralizers. Pac. J. Math. 34, 379-383 (1970). Fuller, K. R., Camillo, V. (see Camillo and Fuller).Fuller, K. R., Dickson, S. E. (see Dickson and Fuller).Google Scholar
  5. [64]
    Freyd, P.: Abelian Categories. New York: Harper Row 1964.Google Scholar
  6. [71]
    Lambek, J.: Torsion Theories, Additive Semantics, and Rings of Quotients. Lecture Notes in Mathematics, No. 177. Berlin/Heidelberg/New York: Springer 1971. Lambek, J., Findlay, G. D. (see Findlay and Lambek).Google Scholar

Copyright information

© Springer-Verlag, Berlin · Heidelberg 1973

Authors and Affiliations

  • Carl Faith
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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