LEADER 03749nam 2200637 a 450 001 9910438153403321 005 20250820221807.0 010 $a1-283-63150-4 010 $a9786613943958 010 $a3-642-31712-X 024 7 $a10.1007/978-3-642-31712-5 035 $a(CKB)2670000000253979 035 $a(EBL)994006 035 $a(OCoLC)810935703 035 $a(SSID)ssj0000767021 035 $a(PQKBManifestationID)11423972 035 $a(PQKBTitleCode)TC0000767021 035 $a(PQKBWorkID)10731262 035 $a(PQKB)10035852 035 $a(DE-He213)978-3-642-31712-5 035 $a(MiAaPQ)EBC994006 035 $a(PPN)168320118 035 $a(EXLCZ)992670000000253979 100 $a20120822d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFactoring ideals in integral domains /$fMarco Fontana, Evan Houston, Thomas Lucas 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (169 p.) 225 0$aLecture notes of the Unione Matematica Italiana,$x1862-9113 ;$v14 300 $aDescription based upon print version of record. 311 08$a3-642-31711-1 320 $aIncludes bibliographical references and index. 327 $aFactoring Ideals in Integral Domains; Preface; Contents; Chapter 1 Introduction; Chapter 2 Sharpness and Trace Properties; 2.1 h-Local Domains; 2.2 Sharp and Double Sharp Domains; 2.3 Sharp and Antesharp Primes; 2.4 Trace Properties; 2.5 Sharp Primes and Intersections; Chapter 3 Factoring Ideals in Almost Dedekind Domains and Generalized Dedekind Domains; 3.1 Factoring with Radical Ideals; 3.2 Factoring Families for Almost Dedekind Domains; 3.3 Factoring Divisorial Ideals in Generalized Dedekind Domains; 3.4 Constructing Almost Dedekind Domains 327 $aChapter 4 Weak, Strong and Very Strong Factorization4.1 History; 4.2 Weak Factorization; 4.3 Overrings and Weak Factorization; 4.4 Finite Divisorial Closure; Chapter 5 Pseudo-Dedekind and Strong Pseudo-Dedekind Factorization; 5.1 Pseudo-Dedekind Factorization; 5.2 Local Domains with Pseudo-Dedekind Factorization; 5.3 Strong Pseudo-Dedekind Factorization; 5.4 Factorization and the Ring R(X); Chapter 6 Factorization and Intersections of Overrings; 6.1 h-Local Maximal Ideals; 6.2 Independent Pairs of Overrings; 6.3 Jaffard Families and Matlis Partitions; 6.4 Factorization Examples 327 $aSymbols and DefinitionsReferences; Index 330 $aThis volume provides a wide-ranging survey of, and many new results on, various important types of ideal factorization actively investigated by several authors in recent years.  Examples of domains studied include (1) those with weak factorization, in which each nonzero, nondivisorial ideal can be factored as the product of its divisorial closure and a product of maximal ideals and (2) those with pseudo-Dedekind factorization, in which each nonzero, noninvertible ideal can be factored as the product of an invertible ideal with a product of pairwise comaximal prime ideals.  Prüfer domains play a central role in our study, but many non-Prüfer examples are considered as well. 410 0$aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v14 606 $aIntegral domains 615 0$aIntegral domains. 676 $a512.7 700 $aFontana$b Marco$047443 701 $aHouston$b Evan$f1948-$0283856 701 $aLucas$b Tom$g(Thomas)$01868800 712 02$aUnione matematica italiana. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438153403321 996 $aFactoring ideals in integral domains$94476823 997 $aUNINA