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001			EBC5295322
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005			20240729131757.0
006			m o d |
007			cr cnu||||||||
008			240724s2014 xx o ||||0 eng d
020			_a9781470418922 _q(electronic bk.)
020			_z9780821898451
035			_a(MiAaPQ)EBC5295322
035			_a(Au-PeEL)EBL5295322
035			_a(OCoLC)890463461
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA188 .S45 2014
082	0		_a512.9/434
100	1		_aSemrl, Peter.
245	1	4	_aThe Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2014.
264		4	_c©2014.
300			_a1 online resource (86 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.232
505	0		_aCover -- Title page -- Chapter 1. Introduction -- Chapter 2. Notation and basic definitions -- Chapter 3. Examples -- Chapter 4. Statement of main results -- Chapter 5. Proofs -- 5.1. Preliminary results -- 5.2. Splitting the proof of main results into subcases -- 5.3. Square case -- 5.4. Degenerate case -- 5.5. Non-square case -- 5.6. Proofs of corollaries -- Acknowledgments -- Bibliography -- Back Cover.
520			_aHua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\times n matrices over a division ring \mathbb{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 not 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 cannot be extended to the non-square case.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aGeometry, Algebraic.
650		0	_aMatrices.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aSemrl, Peter _tThe Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices _dProvidence : American Mathematical Society,c2014 _z9780821898451
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5295322 _zClick to View
999			_c136278 _d136278