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Some Related Algebraic Structures

  • K. N. Srinivasa Rao
Part of the Texts and Readings in Physical Sciences book series

Abstract

Let R be an additive abelian group containing elements 0, a, b, c, …. It is called a ring if it is also closed with respect to a second composition called multiplication which is both associative and distributive. Thus, the elements of a ring R must, in addition to the axioms (1.2.1a) of Section 1.2, also satisfy the following requirements:
  1. (i)

    aR; bRabR for any a, b.

     
  2. (ii)

    a(bc) = (ab)c for any a, b, cR.

     
  3. (iii)

    a(b + c) = ab + ac and (b + c)a = ba + ca.

     

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References

  1. 1.
    A. Kurosh, Higher Algebra, translated from the Russian by George Yankovksy, Moscow, Mir Publishers, 1972.zbMATHGoogle Scholar
  2. 2.
    B.L. Van der Waerden, Modern algebra vols I,II, (In part a development from lectures by E. Artin and E. Noether) New York, F. Ungar, c1950–c1953Google Scholar
  3. 3.
    B.G. Wybourne, Classical groups for physicists, New York, Wiley, 1974.zbMATHGoogle Scholar

Copyright information

© Hindustan Book Agency 2006

Authors and Affiliations

  • K. N. Srinivasa Rao
    • 1
  1. 1.BangaloreIndia

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