Abstract: | 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. |