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Modules over Noncommutative Rings

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

Abstract

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).

Keywords

Commutative Ring Left Ideal Finite Length Group Algebra Division Algebra 
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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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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