000			03960nam a22004815i 4500
001			978-0-387-92716-9
003			DE-He213
005			20140220082758.0
007			cr nn 008mamaa
008			130719s2013 xxu| s |||| 0|eng d
020			_a9780387927169 _9978-0-387-92716-9
024	7		_a10.1007/978-0-387-92716-9 _2doi
050		4	_aQA150-272
072		7	_aPBF _2bicssc
072		7	_aMAT002000 _2bisacsh
082	0	4	_a512 _223
100	1		_aBirkenmeier, Gary F. _eauthor.
245	1	0	_aExtensions of Rings and Modules _h[electronic resource] / _cby Gary F. Birkenmeier, Jae Keol Park, S Tariq Rizvi.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXX, 432 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreliminaries and Basic Results -- Injectivity and Some of Its Generalizations -- Baer, Rickart, and Quasi-Baer Rings -- Baer, Quasi-Baer Modules, and Their Applications -- Triangular Matrix Representations and Triangular Matrix Extensions -- Matrix, Polynomial, and Group Ring Extensions -- Essential Overring Extensions - Beyond the Maximal Ring of Quotients -- Ring and Module Hulls -- Hulls of Ring Extensions.-  Applications to Rings of Quotients and C* Algebras -- Open Problems and Questions -- References -- Index.
520			_aThe focus of this monograph is the study of rings and modules which have a rich supply of direct summands with respect to various extensions. The first four chapters of the book discuss rings and modules which generalize injectivity (e.g., extending modules), or for which certain annihilators become direct summands (e.g., Baer rings). Ring extensions such as matrix, polynomial, group ring, and essential extensions of rings from the aforementioned classes are considered in the next three chapters. A theory of ring and module hulls relative to a specific class of rings or modules is introduced and developed in the following two chapters. While applications of the results presented can be found throughout the book, the final chapter mainly consists of applications to algebra and functional analysis. These include obtaining characterizations of rings of quotients as direct products of prime rings and descriptions of certain C*-algebras via (quasi-)Baer rings. Extensions of Rings and Modules introduces for the first time in book form: * Baer, quasi-Baer, and Rickart modules   * The theory of generalized triangular matrix rings via sets of triangulating idempotents * A discussion of essential overrings that are not rings of quotients of a base ring and Osofsky's study on the self-injectivity of the injective hull of a ring * Applications of the theory of quasi-Baer rings to C*-algebras Each section of the book is enriched with examples and exercises which make this monograph useful not only for experts but also as a text for advanced graduate courses. Historical notes appear at the end of each chapter, and a list of Open Problems and Questions is provided to stimulate further research in this area. With over 400 references, Extensions of Rings and Modules will be of interest to researchers in algebra and analysis and to advanced graduate students in mathematics.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aMatrix theory.
650		0	_aFunctional analysis.
650	1	4	_aMathematics.
650	2	4	_aAlgebra.
650	2	4	_aFunctional Analysis.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
700	1		_aPark, Jae Keol. _eauthor.
700	1		_aRizvi, S Tariq. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387927152
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-92716-9
912			_aZDB-2-SMA
999			_c94201 _d94201