## Algebraic structures of some sets of Pythagorean triples. II.(English)Zbl 1119.13301

Summary: A natural bijection from $$\mathbb{Z}^2$$ to the set of all Pythagorean triples $$\mathcal P=\{(a,b,c)\in \mathbb{Z}^3 : a^2+b^2=c^2 \}$$ is given. Consequently, all algebraic structures are carried in a natural way to $$\mathcal P$$. This solves the problem of defining ring operations under which $$\mathcal P$$ is essentially a different ring than the one constructed by B. Dawson.
[For part I, see Missouri J. Math. Sci. 12, No. 1 (2000; Zbl 1119.13300).]

### MSC:

 13A99 General commutative ring theory 11D09 Quadratic and bilinear Diophantine equations

Zbl 1119.13300