The group of Pythagorean triples in number fields (Q1191327)

Let \(K\) be an algebraic number field not containing \(i\). A group structure is introduced in the set of solutions of \(x^ 2+y^ 2=1\) \((x,y\in K)\) and the properties of the group so obtained (which is isomorphic to the group of elements with relative norm 1 in \(K(i))\) are studied. The authors deal actually with equivalence classes of solutions of the equation \(x^ 2+y^ 2=z^ 2\) in the ring of integers of \(K\).