A body is a special
ring (short: a ring is an
algebraic structure with two
binary operations, one, the
addition, forms a commutative
group, the other , the
multiplication, forms a
monoid and both
operations are
distributive. for more information, follow the hard-link to
Noether's wu).
The special thing about this ring is, that for the
multiplication exists an
inverse:
(R,+,*) is a body
For x ∈ R AND x ≠ 0
exist an element x^-1 ∈ R with x * x^-1 = x^-1 * x = e
e is the one element, which means x * e = x
(Q,+,*) is such a special ring, whereas the example out of the ring node, (Z,*,+), is just a normal (but commutative) ring.