LEADER 03467nam  22006255  450 
001 996466512503316
005 20200702111416.0
010   $a1-280-39178-2
010   $a9786613569707
010   $a3-642-13368-1
024 7 $a10.1007/978-3-642-13368-8
035   $a(CKB)2550000000015812
035   $a(SSID)ssj0000450490
035   $a(PQKBManifestationID)11298204
035   $a(PQKBTitleCode)TC0000450490
035   $a(PQKBWorkID)10434894
035   $a(PQKB)11501715
035   $a(DE-He213)978-3-642-13368-8
035   $a(MiAaPQ)EBC3065515
035   $a(PPN)149078560
035   $a(EXLCZ)992550000000015812
100   $a20100716d2010      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 14$aThe Use of Ultraproducts in Commutative Algebra$b[electronic resource] /$fby Hans Schoutens
205   $a1st ed. 2010.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010.
215   $a1 online resource (X, 210 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1999
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-13367-3 
320   $aIncludes bibliographical references (p. 193-197) and index.
327   $aUltraproducts and ?o?? Theorem -- Flatness -- Uniform Bounds -- Tight Closure in Positive Characteristic -- Tight Closure in Characteristic Zero. Affine Case -- Tight Closure in Characteristic Zero. Local Case -- Cataproducts -- Protoproducts -- Asymptotic Homological Conjectures in Mixed Characteristic.
330   $aIn spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1999
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgebraic geometry
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgebraic geometry.
615 14$aCommutative Rings and Algebras.
615 24$aAlgebraic Geometry.
676   $a512
686   $a60G51$a60E07$a60J80$a45K05$a65N30$a28A78$a60H05$a60G57$a60J75$a26A33$2msc
700   $aSchoutens$b Hans$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478944
906   $aBOOK
912   $a996466512503316
996   $aUse of ultraproducts in commutative algebra$9261768
997   $aUNISA