Modules over Noncommutative Rings

  • Igor R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 11)


A module over an arbitrary ring R is defined in the same way as in the case of a commutative ring: it is a set M such that for any two elements x, yM, the sum x + y is defined, and for xM and aR the product axM is defined, satisfying the following conditions (for all x, y, zM, a, bR).


Commutative Ring Left Ideal Finite Length Group Algebra Division Algebra 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of ScienceMoscowRussia

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