Methods of constructing hyperfields (Q1072597)

The following construction of hyperfields which contain subhyperfields that are nonisomorphic to quotient hyperfields is given in the paper: Let \(H=G\cup \{0\}\) be a semigroup with zero with respect to a binary multiplication, (G,.) being a group. Define the hypercomposition \(+\) by: \(x+y=\{x,y\}\), if \(x\neq y\), \(x\neq 0\), \(y\neq 0\); \(x+*=H\setminus \{x\}\), if \(x=0\); \(x+0=0+x=\{x\}\), for every \(x\in H\). Then \((H,+,.)\) is such a hyperfield.