Some Related Algebraic Structures

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


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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  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

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© Hindustan Book Agency 2006

Authors and Affiliations

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

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