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On quaternion algebras

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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.

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Literature Cited

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Authors
  1. A. A. Tuganbaev
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Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 209–214, 1994.

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Tuganbaev, A.A. On quaternion algebras. J Math Sci 75, 1750–1753 (1995). https://doi.org/10.1007/BF02368673

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  • DOI: https://doi.org/10.1007/BF02368673

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