000			03217nam a22004215i 4500
001			978-0-387-72766-0
003			DE-He213
005			20250710084015.0
007			cr nn 008mamaa
008			110827s2011 xxu| s |||| 0|eng d
020			_a9780387727660 _a99780387727660
024	7		_a10.1007/978-0-387-72766-0 _2doi
082	0	4	_a512 _223
100	1		_aUnderwood, Robert G. _eauthor.
245	1	3	_aAn Introduction to Hopf Algebras _h[recurso electrónico] / _cby Robert G. Underwood.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2011.
300			_aXIV, 273p. 3 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- Some Notation -- 1. The Spectrum of a Ring.-2. The Zariski Topology on the Spectrum.-3. Representable Group Functors.-4. Hopf Algebras. -5. Larson Orders.-6. Formal Group Hopf Orders.-7. Hopf Orders in KC_p.-8. Hopf Orders in KC_{p^2}.-9. Hopf Orders in KC_{p^3}.-10. Hopf Orders and Galois Module Theory.-11. The Class Group of a Hopf Order.-12. Open Questions and Research Problems.-Bibliography.-Index.
520			_aThe study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging  connections to fields from theoretical physics to computer science. This text is unique in making this engaging subject accessible to advanced graduate and beginning graduate students and focuses on applications of Hopf algebras to algebraic number theory and Galois  module theory, providing a smooth transition from modern algebra to Hopf algebras. After providing an introduction to the spectrum of a ring and the Zariski topology, the text treats presheaves, sheaves, and representable group functors.  In this way the student transitions smoothly from basic algebraic geometry to Hopf algebras.  The importance of Hopf orders is underscored with applications to algebraic number theory, Galois module theory and the theory of formal groups. By the end of the book, readers will be familiar with established results in the field and ready to pose research questions of their own. An exercise set is included in each of twelve chapters with questions ranging in difficulty. Open problems and research questions are presented in the last chapter. Prerequisites include an understanding of the  material on groups, rings, and fields normally covered in a basic course in modern algebra.
650		0	_aMATHEMATICS.
650		0	_aALGEBRA.
650		0	_aGROUP THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aALGEBRA.
650	2	4	_aCOMMUTATIVE RINGS AND ALGEBRAS.
650	2	4	_aGROUP THEORY AND GENERALIZATIONS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387727653
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-72766-0 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c58393 _d58393