03001nam 2200517 450 99649516810331620230421114506.09783031148699(electronic bk.)9783031148682(MiAaPQ)EBC7123169(Au-PeEL)EBL7123169(CKB)25201561300041(PPN)265855349(EXLCZ)992520156130004120230309d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe characterization of finite elasticities factorization theory in Krull monoids via convex geometry /David J. GrynkiewiczCham, Switzerland :Springer,[2022]©20221 online resource (291 pages)Lecture notes in mathematicsPrint version: Grynkiewicz, David J. The Characterization of Finite Elasticities Cham : Springer International Publishing AG,c2022 9783031148682 Includes bibliographical references and index.Intro -- 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.Lecture notes in mathematics (Springer-Verlag)Convex geometryMonoidsGeometria convexathubMonoidesthubLlibres electrònicsthubConvex geometry.Monoids.Geometria convexaMonoides516.08Grynkiewicz David J.1978-1337905MiAaPQMiAaPQMiAaPQ996495168103316The characterization of finite elasticities3057590UNISA