Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

<-- Previous | Newer --> | Current: 983898757 RoseParks at Tue, 06 Mar 2001 17:12:37 +0000.

Fields A field is a RinG in which * is commutative and the nonzero elements form a GrouP under *. A more useable definition is the following: The field (R,+,*) contains a set (R) and two binary operators (+,*) such that: # + is associative: a+(b+c) = (a+b)+c # + has an "zero" z, written 0, such that a+z = z+a = a # for each a in R there is an opposite -a such that a + (-a) = (-a) + a = 0 # for all a, b in R: a+b = b+a # * is associative: a*(b*c) = (a*b)*c # * has an identity e, written 1, such that for all non-zero a: a * 1 = 1 * a = a # each non-zero element a has an inverse, inv(a), such that a * inv(a) = inv(a) * a = 1 # for all a and b, a*b = b*a # for all a,b,c: a*(b+c) = a*b + a*c and (b+c)*a = b*a + c*a ----We already have a page "FielD" with the same material. What do we do? RoseParks