03844nam 2200649 450 991048101580332120170822144148.01-4704-0432-X(CKB)3360000000465015(EBL)3114065(SSID)ssj0000973307(PQKBManifestationID)11553109(PQKBTitleCode)TC0000973307(PQKBWorkID)10959952(PQKB)10243711(MiAaPQ)EBC3114065(PPN)195417194(EXLCZ)99336000000046501520050324h20052005 uy| 0engur|n|---|||||txtccrThe complete dimension theory of partially ordered systems with equivalence and orthogonality /K.R. Goodearl, F. WehrungProvidence, Rhode Island :American Mathematical Society,[2005]©20051 online resource (134 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 831"Volume 176, number 831 (third of 5 numbers)."0-8218-3716-8 Includes bibliographical references (pages 111-113) and index.""Contents""; ""Chapter 1. Introduction""; ""1-1. Background""; ""1-2. Results and methods""; ""1-3. Notation and terminology""; ""Chapter 2. Partial commutative monoids""; ""2-1. Basic results about partial commutative monoids""; ""2-2. Direct decompositions of partial refinement monoids""; ""2-3. Projections of partial refinement monoids""; ""2-4. General comparability""; ""2-5. Boolean-valued partial refinement monoids""; ""2-6. Least and largest difference functions""; ""Chapter 3. Continuous dimension scales""; ""3-1. Basic propertiesthe monoids Z[sub(γ)], R[sub(γ)], and 2[sub(γ)]""""3-2. Dedekind complete lattice-ordered groups""; ""3-3. Continuous functions on extremally disconnected topological spaces""; ""3-4. Completeness of the Boolean algebra of projections""; ""3-5. The elements (p | α)""; ""3-6. The dimension function Î?""; ""3-7. Projections on the directly finite elements""; ""3-8. Embedding arbitrary continuous dimension scales""; ""3-9. Uniqueness of the canonical embedding""; ""3-10. Continuous dimension scales which are proper classes""; ""Chapter 4. Espaliers""; ""4-1. The axioms""""4-2. Purely infinite elements trim sequences""; ""4-3. Axiom (M6)""; ""4-4. D-universal classes of espaliers""; ""4-5. Existence of large constants""; ""Chapter 5. Classes of espaliers""; ""5-1. Abstract measure theory; Boolean espaliers""; ""5-2. Conditionally complete, meet-continuous, relatively complemented, modular lattices""; ""5-3. Self-injective regular rings and nonsingular injective modules""; ""5-4. Projection lattices of W*- and AW*-algebras""; ""5-5. Concluding remarks""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""""L""""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""X""; ""Z""Memoirs of the American Mathematical Society ;no. 831.Lattice theoryBoolean ringsPartial algebrasModules (Algebra)Electronic books.Lattice theory.Boolean rings.Partial algebras.Modules (Algebra)510 s511.3/3Goodearl K. R.57894Wehrung F(Friedrich),1961-MiAaPQMiAaPQMiAaPQBOOK9910481015803321The complete dimension theory of partially ordered systems with equivalence and orthogonality1909457UNINA00803nam a22002171i 450099100380737970753620040611154314.0040802s1894 fr |||||||||||||||||fre b13131217-39ule_instARCHE-108382ExLBiblioteca InterfacoltàitaA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l.Maizeroy, René467362Ville d'amour /René MaizeroyParis :Ollendorff,1894242 p. ;19 cm.b1313121702-04-1405-08-04991003807379707536LE002 Fondo Giudici P 12441LE002G-14969le002C. 1-E0.00-no 00000.i1376751305-08-04Ville d'amour308996UNISALENTOle00205-08-04ma -frefr 01