On quaternion algebras

It is proved that the distributiveness of the right ideals lattice for a quaternion algebra over a commutative ring A is equivalent to the following property: the equation x²+y²+z²=0 is uniquely solvable in the field A/M for any maximal ideals M of A, the lattice of the ideals of A being distributive. Bibliography: 5 titles. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 209–214, 1994.