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Algebra pp 83-116 | Cite as

Rings

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 211)

Abstract

A ring A is a set, together with two laws of composition called multiplication and addition respectively, and written as a product and as a sum respectively, satisfying the following conditions:
  1. RI 1.

    With respect to addition, A is a commutative group.

     
  2. RI 2.

    The multiplication is associative, and has a unit element.

     
  3. RI 3.
    For all x, y, zA we have
    $$ (x + y)z = xz + yz and z(x + y) = zx + zy. $$
     

Keywords

Prime Ideal Local Ring Commutative Ring Unit Element Left Ideal 
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 Science+Business Media New York 2002

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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