additive inverse

Thus only the additive identity has an additive inverse in [S.

Semirings satisfy all properties of unital rings except the existence of additive inverses.

Rahn observes that if the nonzero intervals are paired as additive inverses (mod 7) to form the three interval classes (1, 6), (2, 5), (3, 4), then each of the two cycles .

p](a) = (p - 1) / 2, each member of A is coprime with p; it follows that each member of A'(which contains the additive inverses (mod p) of all elements in A) is coprime with p.

The diagrams are arranged to exhibit inversional relationships: additive inverses (mod p) are placed in symmetrical positions on the two circles (Example 3 (i)) or upper and lower parts of the figure-eight (Example 3 (ii) and (iii)).