Equivalence and Duality for Module Categories

  • Frank W. Anderson
  • Kent R. Fuller
Part of the Graduate Texts in Mathematics book series (GTM, volume 13)


So far our emphasis has been on studying rings in terms of the module categories they admit—that is, in terms of the representations of the rings as endomorphism rings of abelian groups. As we shall see the Wedderburn Theorem for simple artinian rings can be interpreted as asserting that a ring R is simple artinian if and only if the category R M is “the same” as the category D M for some division ring D. On the other hand, if D is a division ring, then the theory of duality from elementary linear algebra asserts that the categories D FM and FM D of finitely generated left D-vector spaces and right D-vector spaces are “duals” of one another.


Full Subcategory Projective Module Module Category Division Ring Natural Isomorphism 


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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Frank W. Anderson
    • 1
  • Kent R. Fuller
    • 2
  1. 1.Department of MathematicsUniversity of OregonEugeneUSA
  2. 2.Division of Mathematical SciencesThe University of IowaIowa CityUSA

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