000			04523nam a22004693i 4500
001			EBC3114442
003			MiAaPQ
005			20240729124608.0
006			m o d |
007			cr cnu||||||||
008			240724s2001 xx o ||||0 eng d
020			_a9781470402983 _q(electronic bk.)
020			_z9780821826188
035			_a(MiAaPQ)EBC3114442
035			_a(Au-PeEL)EBL3114442
035			_a(CaPaEBR)ebr11041220
035			_a(OCoLC)922965064
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA247.3 -- .K73 2001eb
082	0		_a510 s;512/.74
100	1		_aKrause, Henning.
245	1	0	_aSpectrum of a Module Category.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2001.
264		4	_c©2001.
300			_a1 online resource (143 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.149
505	0		_aIntro -- Contents -- Chapter 0. Introduction -- Chapter 1. The functor category -- 1.1. Preliminaries -- 1.2. Purity -- Chapter 2. Definable subcategories -- 2.1. Definable subcategories -- 2.2. Saturation -- 2.3. The Ziegler topology -- 2.4. Definable quotient categories -- 2.5. Examples -- Chapter 3. Left approximations -- 3.1. Left almost split maps -- 3.2. Left approximations -- 3.3. Minimal left approximations -- Chapter 4. Duality -- 4.1. Purely equivalent and purely opposed modules -- 4.2. The dual of a definable subcategory -- 4.3. Pure-reflexive modules -- Chapter 5. Ideals in the category of finitely presented modules -- 5.1. Fp-idempotent ideals -- 5.2. Ideals generated by idempotents -- Chapter 6. Endofinite modules -- 6.1. The endocategory of a module -- 6.2. ∑-pure-injective modules -- 6.3. Product-complete modules -- 6.4. Endofinite modules -- 6.5. Generic modules -- 6.6. Ideals of finite length -- Chapter 7. Krull-Gabriel dimension -- 7.1. The Krull-Gabriel dimension of a ring -- 7.2. The Krull-Gabriel dimension of a module -- Chapter 8. The infinite radical -- 8.1. The preinjective dimension of a module -- 8.2. Transfinite powers of the Jacobson radical -- Chapter 9. Functors between module categories -- 9.1. Coherent functors -- Chapter 10. Tame algebras -- 10.1. Endofinitely tame algebras -- 10.2. Functors preserving tameness -- 10.3. Representation embeddings -- 10.4. One-parameter families and generic modules -- Chapter 11. Rings of definable scalars -- 11.1. Rings of definable scalars -- 11.2. Calculus of fractions -- 11.3. Biendomorphism rings -- 11.4. Basic properties -- 11.5. Epimorphisms of rings -- Chapter 12. Reflective definable subcategories -- 12.1. Reflective definable subcategories -- 12.2. Φ-continuous modules -- 12.3. Definable and universal localizations -- Chapter 13. Sheaves.
505	8		_a13.1. Sheaves on the Gabriel spectrum -- 13.2. The Zariski topology -- 13.3. Structure sheaves -- 13.4. Associated sheaves of modules -- Chapter 14. Tame hereditary algebras -- 14.1. Preliminaries -- 14.2. A parametrizing curve -- Chapter 15. Coherent rings -- 15.1. Preliminaries -- 15.2. Prime spectrum versus Gabriel spectrum -- 15.3. The global section functor -- Appendix A. Locally coherent Grothendieck categories -- A.1. Localization in abelian categories -- A.2. Locally coherent Grothendieck categories -- A.3. Localization in locally coherent Grothendieck categories -- A.4. Locally noetherian categories -- Appendix B. Dimensions -- B.1. The dimension of an abelian category -- B.2. The dimension of a modular lattice -- Appendix C. Finitely presented functors and ideals -- C.1. The category of finitely presented functors -- C.2. Ideals in additive categories -- Bibliography.
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	_aInjective modules (Algebra).
650		0	_aCategories (Mathematics).
655		4	_aElectronic books.
776	0	8	_iPrint version: _aKrause, Henning _tSpectrum of a Module Category _dProvidence : American Mathematical Society,c2001 _z9780821826188
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114442 _zClick to View
999			_c69937 _d69937