High Quality Content by WIKIPEDIA articles! In mathematics a near-field is an algebraic structure similar to a division ring, except that it has only one of the two distributive laws. Alternatively, a near-field is a near-ring in which there is a multiplicative identity, and every non-zero element has a multiplicative inverse.The concept of a near-field was first introduced by L.E. Dickson in 1905. He took division rings and modified their multiplication, while leaving addition as it was, and thus produced the first known examples of near-fields that were not division rings. The near-fields produced by this method are known as Dickson near-fields; the near-field of order 9 given above is a Dickson near-field. Zassenhaus proved that all but 7 finite near-fields are either division rings or Dickson near-fields.

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