Linear equations and heights over division algebras |
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| Authors: | Christine Liebendörfer |
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| Institution: | Institut de Mathématiques Bernoulli, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland |
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| Abstract: | We make a start on the investigation of “small” solutions to systems of homogeneous linear equations over non-commutative division algebras. In this paper we prove some upper and lower bounds for the sizes of solutions to such systems. To measure solutions and coefficient matrices we define heights which satisfy natural invariance and finiteness properties. |
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| Keywords: | Heights Division algebras Quaternion algebras Linear equations |
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