LEADER 05302 am 22007093u 450 001 9910320751903321 005 20200520144314.0 010 $a1-280-56956-5 010 $a9786613599162 010 $a3-11-027860-X 024 7 $a10.1515/9783110278606 035 $a(CKB)2550000000101202 035 $a(EBL)913344 035 $a(OCoLC)795120010 035 $a(SSID)ssj0000678824 035 $a(PQKBManifestationID)11405300 035 $a(PQKBTitleCode)TC0000678824 035 $a(PQKBWorkID)10745546 035 $a(PQKB)11487800 035 $a(DE-B1597)175264 035 $a(OCoLC)853262728 035 $a(DE-B1597)9783110278606 035 $a(Au-PeEL)EBL913344 035 $a(CaPaEBR)ebr10562611 035 $a(CaONFJC)MIL359916 035 $a(ScCtBLL)d3954c92-12a7-4bb4-b84e-e24b2703d6ef 035 $a(MiAaPQ)EBC913344 035 $a(EXLCZ)992550000000101202 100 $a20120612d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aClosures, finiteness and factorization$b[electronic resource] /$fedited by Christopher Francisco ... [et al.] 210 $aBerlin $cDe Gruyter$d2012 215 $a1 online resource (328 p.) 225 0 $aProgress in commutative algebra ;$v2 300 $a"This collection of papers in commutative algebra stemmed out of the 2009 Fall Southeastern American Mathematical Society Meeting ..."--P. [v]. 311 $a3-11-027859-6 320 $aIncludes bibliographical references. 327 $t Frontmatter -- $tPreface -- $tContents -- $tA Guide to Closure Operations in Commutative Algebra / $rEpstein, Neil -- $tA Survey of Test Ideals / $rSchwede, Karl / Tucker, Kevin -- $tFinite-dimensional Vector Spaces with Frobenius Action / $rEnescu, Florian -- $tFiniteness and Homological Conditions in Commutative Group Rings / $rGlaz, Sarah / Schwarz, Ryan -- $tRegular Pullbacks / $rBoynton, Jason G. / Sather-Wagstaff, Sean -- $tNoetherian Rings without Finite Normalization / $rOlberding, Bruce -- $tKrull Dimension of Polynomial and Power Series Rings / $rWatkins, John J. -- $tThe Projective Line over the Integers / $rCelikbas, Ela / Eubanks-Turner, Christina -- $tOn Zero Divisor Graphs / $rCoykendall, Jim / Sather-Wagstaff, Sean / Sheppardson, Laura / Spiroff, Sandra -- $tA Closer Look at Non-Unique Factorization via Atomic Decay and Strong Atoms / $rChapman, Scott T. / Krause, Ulrich 330 $aThis is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 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. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization. 410 0$aDe Gruyter Proceedings in Mathematics. 606 $aCommutative algebra 610 $aClosure. 610 $aCommutative Algebra. 610 $aDecomposition. 610 $aFactorization. 615 0$aCommutative algebra. 676 $a512 676 $a512.24 676 $a512/.24 701 $aFrancisco$b Christopher$0919310 712 12$aSoutheastern American Mathematical Society Meeting$f(2009) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910320751903321 996 $aClosures, finiteness and factorization$92061823 997 $aUNINA