Direct Sums and Products

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


For each ring R we have derived several module categories—among these the category R M of left R-modules. This derivation is not entirely reversible for, in general, R M does not characterize R. However, as we shall see in Chapter 6 it does come close. Thus, we can expect to uncover substantial information about R by mining R M. So in this chapter we start to probe more deeply into the structure of the modules themselves. In so far as possible we propose to do this in the context of the category R M for in this way at any subsequent stage we shall be able to apply the general machinery of category theory.


Direct Summand Left Ideal Subdirect Product Primitive Idempotent Central Idempotent 


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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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