LEADER 03001nam 2200517 450 001 996495168103316 005 20230421114506.0 010 $a9783031148699$b(electronic bk.) 010 $z9783031148682 035 $a(MiAaPQ)EBC7123169 035 $a(Au-PeEL)EBL7123169 035 $a(CKB)25201561300041 035 $a(PPN)265855349 035 $a(EXLCZ)9925201561300041 100 $a20230309d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe characterization of finite elasticities $efactorization theory in Krull monoids via convex geometry /$fDavid J. Grynkiewicz 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (291 pages) 225 1 $aLecture notes in mathematics 311 08$aPrint version: Grynkiewicz, David J. The Characterization of Finite Elasticities Cham : Springer International Publishing AG,c2022 9783031148682 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Introduction -- 1.1 Convex Geometry -- 1.2 Krull Domains, Transfer Krull Monoids and Factorization -- 1.3 Zero-Sum Sequences -- 1.4 Overview of Main Results -- 2 Preliminaries and General Notation -- 2.1 Convex Geometry -- 2.2 Lattices and Partially Ordered Sets -- 2.3 Sequences and Rational Sequences -- 2.4 Arithmetic Invariants for Transfer Krull Monoids -- 2.5 Asymptotic Notation -- 3 Asymptotically Filtered Sequences, Encasement and Boundedness -- 3.1 Asymptotically Filtered Sequences -- 3.2 Encasement and Boundedness -- 4 Elementary Atoms, Positive Bases and Reay Systems -- 4.1 Basic Non-degeneracy Characterizations -- 4.2 Elementary Atoms and Positive Bases -- 4.3 Reay Systems -- 4.4 -Filtered Sequences, Minimal Encasement and Reay Systems -- 5 Oriented Reay Systems -- 6 Virtual Reay Systems -- 7 Finitary Sets -- 7.1 Core Definitions and Properties -- 7.2 Series Decompositions and Virtualizations -- 7.3 Finiteness Properties of Finitary Sets -- 7.4 Interchangeability and the Structure of X(G0) -- 8 Factorization Theory -- 8.1 Lambert Subsets and Elasticity -- 8.2 The Structure of Atoms and Arithmetic Invariants -- Summary -- 8.3 Transfer Krull Monoids Over Subsets of Finitely Generated Abelian Groups -- Summary -- References -- Index. 410 0$aLecture notes in mathematics (Springer-Verlag) 606 $aConvex geometry 606 $aMonoids 606 $aGeometria convexa$2thub 606 $aMonoides$2thub 608 $aLlibres electrònics$2thub 615 0$aConvex geometry. 615 0$aMonoids. 615 7$aGeometria convexa 615 7$aMonoides 676 $a516.08 700 $aGrynkiewicz$b David J.$f1978-$01337905 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996495168103316 996 $aThe characterization of finite elasticities$93057590 997 $aUNISA