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| 001 | 978-3-031-77453-9 | ||
| 003 | DE-He213 | ||
| 005 | 20251030114605.0 | ||
| 007 | cr nn 008mamaa | ||
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_a10.1007/978-3-031-77453-9 _2doi |
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_aMAT002010 _2bisacsh |
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_aPBF _2thema |
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| 100 | 1 |
_aChristensen, Lars Winther. _eauthor. _0(orcid)0000-0002-9360-123X _1https://orcid.org/0000-0002-9360-123X _4aut _4http://id.loc.gov/vocabulary/relators/aut _988588 |
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| 245 | 1 | 0 |
_aDerived Category Methods in Commutative Algebra _h[electronic resource] / _cby Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2024. |
|
| 300 |
_aXXIII, 1119 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSpringer Monographs in Mathematics, _x2196-9922 |
|
| 505 | 0 | _a1 Modules -- 2 Complexes -- 3 Categorical Constructions -- 4 Equivalences and Isomorphisms -- 5 Resolutions -- 6 The Derived Category -- 7 Derived Functors -- 8 Homological Dimensions -- 9 Gorenstein Homological Dimensions -- 10 Dualizing Complexes -- 11 Torsion and Completion -- 12 A Brief for Commutative Ring Theorists -- 13 Derived Torsion and Completion -- 14 Krull Dimension, Depth, and Width -- 15 Support Theories -- 16 Homological Invariants over Local Rings -- 17 Going Local -- 18 Dualities and Cohen-Macaulay Rings -- 19 Gorenstein Dimensions and Gorenstein Rings -- 20 Global Dimension and Regular Rings -- APPENDIX A: Acyclicity and Boundedness -- APPENDIX B: Minimality -- APPENDIX C: Structure of Injective Modules -- APPENDIX D: Projective Dimension of Flat Modules -- APPENDIX E: Triangulated Categories. | |
| 520 | _aDerived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck’s Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings. The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject. | ||
| 650 | 0 |
_aAlgebra, Homological. _970150 |
|
| 650 | 0 |
_aCommutative algebra. _970151 |
|
| 650 | 0 |
_aCommutative rings. _970152 |
|
| 650 | 1 | 4 |
_aCategory Theory, Homological Algebra. _970155 |
| 650 | 2 | 4 |
_aCommutative Rings and Algebras. _970156 |
| 700 | 1 |
_aFoxby, Hans-Bjørn. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _988589 |
|
| 700 | 1 |
_aHolm, Henrik. _eauthor. _0(orcid)0000-0002-6895-6493 _1https://orcid.org/0000-0002-6895-6493 _4aut _4http://id.loc.gov/vocabulary/relators/aut _988590 |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031774522 |
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_iPrinted edition: _z9783031774546 |
| 830 | 0 |
_aSpringer Monographs in Mathematics, _x2196-9922 _973001 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-77453-9 |
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