LEADER 04863 am 22006613u 450 001 996309225503316 005 20200520144314.0 010 $a1-280-57032-6 010 $a9786613599926 010 $a3-11-025040-3 024 7 $a10.1515/9783110250404 035 $a(CKB)2550000000101203 035 $a(EBL)913268 035 $a(OCoLC)795120008 035 $a(SSID)ssj0000678823 035 $a(PQKBManifestationID)12257178 035 $a(PQKBTitleCode)TC0000678823 035 $a(PQKBWorkID)10729040 035 $a(PQKB)10892595 035 $a(DE-B1597)123218 035 $a(OCoLC)853262028 035 $a(DE-B1597)9783110250404 035 $a(Au-PeEL)EBL913268 035 $a(CaPaEBR)ebr10562593 035 $a(CaONFJC)MIL359992 035 $a(ScCtBLL)b3e2eee2-793c-4533-a3ab-9bcf46e8d3df 035 $a(MiAaPQ)EBC913268 035 $a(EXLCZ)992550000000101203 100 $a20111021d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aProgress in commutative algebra 1$b[electronic resource] $ecombinatorics and homology /$fedited by Christopher Francisco ... [et al.] 210 $aBerlin $cDe Gruyter$d2012 215 $a1 online resource (376 p.) 225 0 $aDe Gruyter Proceedings in Mathematics 300 $aDescription based upon print version of record. 311 $a3-11-025034-9 320 $aIncludes bibliographical references. 327 $t Frontmatter -- $tPreface -- $tTable of Contents -- $tBoij-Söderberg Theory: Introduction and Survey / $rFløystad, Gunnar -- $tHilbert Functions of Fat Point Subschemes of the Plane: the Two-fold Way / $rGeramita, Anthony V. / Harbourne, Brian / Migliore, Juan C. -- $tEdge Ideals: Algebraic and Combinatorial Properties / $rMorey, Susan / Villarreal, Rafael H. -- $tThree Simplicial Resolutions / $rMermin, Jeff -- $tA Minimal Poset Resolution of Stable Ideals / $rClark, Timothy B. P. -- $tSubsets of Complete Intersections and the EGH Conjecture / $rCooper, Susan M. -- $tThe Homological Conjectures / $rRoberts, Paul C. -- $tThe Compatibility, Independence, and Linear Growth Properties / $rYao, Yongwei -- $tRecent Progress in Coherent Rings: a Homological Perspective / $rHummel, Livia -- $tNon-commutative Crepant Resolutions: Scenes From Categorical Geometry / $rLeuschke, Graham J. 330 $aThis is the first 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 combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke. 410 0$aDe Gruyter Proceedings in Mathematics 606 $aCommutative algebra 610 $aCombinatirics. 610 $aCommutative Algebra. 610 $aHomology. 615 0$aCommutative algebra. 676 $a512 701 $aFrancisco$b Christopher$0919310 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996309225503316 996 $aProgress in commutative algebra 1$92204316 997 $aUNISA