Algebra pp 83-116 | Cite as


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


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
    $$ (x + y)z = xz + yz and z(x + y) = zx + zy. $$


Prime Ideal Local Ring Commutative Ring Unit Element Left Ideal 
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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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