
 Field (mathematics) (Site not responding. Last check: 20071105) 
  In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication, and division (except division by zero) may be performed and the associative, commutative, and distributive rules hold, which are familiar from the arithmetic of ordinary numbers. 
  Fields are important objects of study in algebra since they provide the proper generalization of number domains, such as the sets of rational numbers, real numbers, or complex numbers. 
  An algebraic extension of a field F is the smallest field containing F and a root of a irreducible polynomial p(x) in F[x]. 
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