
 Field (mathematics) 
  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. 
  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. 
  For a given field F, the set F(X) of rational functions in the variable X with coefficients in F is a field; this is defined as the set of quotients of polynomials with coefficients in F. 
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