Some Related Algebraic Structures
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:
a ∈ R; b ∈ R ⇒ ab ∈ R for any a, b.
a(bc) = (ab)c for any a, b, c ∈ R.
a(b + c) = ab + ac and (b + c)a = ba + ca.
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- 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
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