Abstract
Solution sets of systems of linear equations over fields are characterized as being affine subspaces. But what can we say about the “shape” of the set of all solutions of other systems of equations? We study solution sets over arbitrary algebraic structures, and we give a necessary condition for a set of n-tuples to be the set of solutions of a system of equations in n unknowns over a given algebra. In the case of Boolean equations we obtain a complete characterization, and we also characterize solution sets of systems of Boolean functional equations.
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Research supported by the Hungarian National Foundation for Scientific Research (Grant Nos. K104251 and K115518) and by the János Bolyai Research Scholarship.
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Tóth, E., Waldhauser, T. On the shape of solution sets of systems of (functional) equations. Aequat. Math. 91, 837–857 (2017). https://doi.org/10.1007/s00010-017-0499-2
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DOI: https://doi.org/10.1007/s00010-017-0499-2