Abelian Groups in Rational Number Theory
Part of the Graduate Texts in Mathematics book series (GTM, volume 77)
In the elementary theory of rational numbers we are constantly dealing with Abelian groups. The set of integers has the properties:
a + b is an integer if a and b are integers; a + b = b + a,
a + (b + c) = (a + b) + c,
If a + b = a′ + b, then a = a′,
For each a and b there is an integer x such that a + x = b.
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© Springer Science+Business Media New York 1981