LEADER 03018nam 2200589 a 450 001 9910483359803321 005 20200520144314.0 010 $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 $a20100614d2010 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe use of ultraproducts in commutative algebra /$fHans Schoutens 205 $a1st ed. 2010. 210 $aNew York $cSpringer$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 (Springer-Verlag) ;$v1999. 606 $aCommutative algebra 606 $aUltraproducts 615 0$aCommutative algebra. 615 0$aUltraproducts. 676 $a512 686 $a60G51$a60E07$a60J80$a45K05$a65N30$a28A78$a60H05$a60G57$a60J75$a26A33$2msc 700 $aSchoutens$b Hans$0478944 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483359803321 996 $aUse of ultraproducts in commutative algebra$9261768 997 $aUNINA