(mathematics) The additive inverse of a real or complex number a is the number which when added to a gives 0; the multiplicative inverse of a is the number which when multiplied with a gives 1. The inverse of a fractional ideal I of an integral domain R is the set of all elements x in the quotient field K of R such that xy is in I for all y in I. For a set S with a binary operation x·y that has an identity element e, the inverse of a member, x, of S is another member, &xmacr;, of S for which x·&xmacr; = &xmacr;·x = e.




