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  Fields are among the fundamental mathematical structures studied in algebra. A field is a ring in which each non-zero member of the field has a multiplicative inverse. The structure is that a field is a group under the operation of addition and (if the zero is left out) also a group under multiplication. Examples of fields include most of the commonly used kinds of numbers: algebraic numbers, complex numbers, rational numbers and real numbers are all fields. Real numbers, in fact, can be uniquely characterized as they are the only field which has an ordering and the property of completeness. SMcL  



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