A double loop consists of a set K and two operations
which satisfy the following axioms.
If (K,T) is a ternary field,
we have an addition x+y:=T(1,x,y) and a multiplication
xy:=T(x,y,0), and K becomes a double loop using these two
- (K,+) is a loop.
is a loop where 0 is
the neutral element of the additive loop (K,+).
- We have 0x=x0=0 for each element x of K.
Contributed by Hauke Klein
Version $Id: double.html,v 1.1 2001/01/17 09:02:39 hauke Exp $