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On the shape of solution sets of systems of (functional) equations.
- Source :
- Aequationes Mathematicae; Oct2017, Vol. 91 Issue 5, p837-857, 21p
- Publication Year :
- 2017
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 91
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 125130755
- Full Text :
- https://doi.org/10.1007/s00010-017-0499-2