000			05774cam a2200661Ii 4500
001			ocn795120010
003			OCoLC
005			20220517104213.0
006			m d
007			cr cnu---unuuu
008			120611s2012 gw o 000 0 eng d
040			_aEBLCP _beng _epn _erda _cEBLCP _dOCLCQ _dN$T _dOCLCQ _dYDXCP _dOCLCQ _dOCLCF _dDEBSZ _dOCLCO _dOCLCQ _dCOO _dOCLCQ _dAGLDB _dVGM _dZCU _dMERUC _dOCLCQ _dDEGRU _dOCLCQ _dVTS _dICG _dSTF _dLEAUB _dDKC _dAU@ _dOCLCQ _dUKAHL _dOCLCQ _dUKKNU _dN$T
020			_a9783110278606 _q(electronic bk.)
020			_a311027860X _q(electronic bk.)
024	7		_a10.1515/9783110278606 _2doi
029	1		_aDEBBG _bBV043096637
029	1		_aDEBBG _bBV044165111
029	1		_aDEBSZ _b397308167
029	1		_aDEBSZ _b421412852
029	1		_aDEBSZ _b431141673
029	1		_aDEBSZ _b478282567
029	1		_aAU@ _b000066528297
029	1		_aAU@ _b000069156959
035			_a(OCoLC)795120010
050		4	_aQA251.3
072		7	_aMAT _x014000 _2bisacsh
082	0	4	_a512.2 _223
049			_aN$TA
245	0	0	_aProgress in commutative algebra. _n2, _pClosures, finiteness and factorization / _cedited by Christopher Francisco [and others].
246	3	0	_aClosures, finiteness and factorization
264		1	_aBerlin ; _aBoston : _bDe Gruyter, _c2012.
300			_a1 online resource (328 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aDe Gruyter Proceedings in mathematics
505	0		_aPreface; A Guide to Closure Operations in Commutative Algebra; 1 Introduction; 2 What Is a Closure Operation?; 2.1 The Basics; 2.2 Not-quite-closure Operations; 3 Constructing Closure Operations; 3.1 Standard Constructions; 3.2 Common Closures as Iterations of Standard Constructions; 4 Properties of Closures; 4.1 Star-, Semi-prime, and Prime Operations; 4.2 Closures Defined by Properties of (Generic) Forcing Algebras; 4.3 Persistence; 4.4 Axioms Related to the Homological Conjectures; 4.5 Tight Closure and Its Imitators; 4.6 (Homogeneous) Equational Closures and Localization.
505	8		_a5 Reductions, Special Parts of Closures, Spreads, and Cores5.1 Nakayama Closures and Reductions; 5.2 Special Parts of Closures; 6 Classes of Rings Defined by Closed Ideals; 6.1 When Is the Zero Ideal Closed?; 6.2 When Are 0 and Principal Ideals Generated by Non-zerodivisors Closed?; 6.3 When Are Parameter Ideals Closed (Where R Is Local)?; 6.4 When Is Every Ideal Closed?; 7 Closure Operations on (Sub)modules; 7.1 Torsion Theories; A Survey of Test Ideals; 1 Introduction; 2 Characteristic p Preliminaries; 2.1 The Frobenius Endomorphism; 2.2 F-purity; 3 The Test Ideal.
505	8		_a3.1 Test Ideals of Map-pairs3.2 Test Ideals of Rings; 3.3 Test Ideals in Gorenstein Local Rings; 4 Connections with Algebraic Geometry; 4.1 Characteristic 0 Preliminaries; 4.2 Reduction to Characteristic p> 0 and Multiplier Ideals; 4.3 Multiplier Ideals of Pairs; 4.4 Multiplier Ideals vs. Test Ideals of Divisor Pairs; 5 Tight Closure and Applications of Test Ideals; 5.1 The Briançon-Skoda Theorem; 5.2 Tight Closure for Modules and Test Elements; 6 Test Ideals for Pairs (R, at) and Applications; 6.1 Initial Definitions of at -test Ideals; 6.2 at -tight Closure; 6.3 Applications.
505	8		_a7 Generalizations of Pairs: Algebras of Maps8 Other Measures of Singularities in Characteristic p; 8.1 F-rationality; 8.2 F-injectivity; 8.3 F-signature and F-splitting Ratio; 8.4 Hilbert-Kunz( -Monsky) Multiplicity; 8.5 F-ideals, F-stable Submodules, and F-pure Centers; A Canonical Modules and Duality; A.1 Canonical Modules, Cohen-Macaulay and Gorenstein Rings; A.2 Duality; B Divisors; C Glossary and Diagrams on Types of Singularities; C.1 Glossary of Terms; Finite-dimensional Vector Spaces with Frobenius Action; 1 Introduction; 2 A Noncommutative Principal Ideal Domain.
505	8		_a3 Ideal Theory and Divisibility in Noncommutative PIDs3.1 Examples in K{F}; 4 Matrix Transformations over Noncommutative PIDs; 5 Module Theory over Noncommutative PIDs; 6 Computing the Invariant Factors; 6.1 Injective Frobenius Actions on Finite Dimensional Vector Spaces over a Perfect Field; 7 The Antinilpotent Case; Finiteness and Homological Conditions in Commutative Group Rings; 1 Introduction; 2 Finiteness Conditions; 3 Homological Dimensions and Regularity; 4 Zero Divisor Controlling Conditions; Regular Pullbacks; 1 Introduction; 2 Some Background; 3 Pullbacks of Noetherian Rings. 4 Pullbacks of Prüfer Rings.
520			_aThis is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions atthe 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theo.
588	0		_aPrint version record.
546			_aIn English.
506	0		_aOpen Access _5EbpS
650		0	_aCommutative algebra.
650		7	_aMATHEMATICS _xGroup Theory. _2bisacsh _927076
650		7	_aCommutative algebra. _2fast _0(OCoLC)fst00871202
655		0	_aElectronic books.
655		4	_aElectronic books.
700	1		_aFrancisco, Christopher.
830		0	_aProceedings in mathematics.
856	4	0	_3EBSCOhost _uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=456811
938			_aEBSCOhost _bEBSC _n456811
942			_cEBK
994			_aC0 _bN$T
999			_c4451 _d4451