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- DescriptionHua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m�n matrices over a division ring D which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is t isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples showing that it cant be extended to the n-square case.
- Author BiographyPeter eemrl , University of Ljubljana, Slovenia.
- Author(s)Peter Semrl
- PublisherAmerican Mathematical Society
- Date of Publication30/10/2014
- Series TitleMemoirs of the American Mathematical Society
- Series Part/Volume Number232
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Width178 mm
- Height254 mm
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