LEADER 03841nam 2200649 450 001 9910827772403321 005 20170822144148.0 010 $a1-4704-0432-X 035 $a(CKB)3360000000465015 035 $a(EBL)3114065 035 $a(SSID)ssj0000973307 035 $a(PQKBManifestationID)11553109 035 $a(PQKBTitleCode)TC0000973307 035 $a(PQKBWorkID)10959952 035 $a(PQKB)10243711 035 $a(MiAaPQ)EBC3114065 035 $a(RPAM)13910920 035 $a(PPN)195417194 035 $a(EXLCZ)993360000000465015 100 $a20050324h20052005 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe complete dimension theory of partially ordered systems with equivalence and orthogonality /$fK.R. Goodearl, F. Wehrung 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2005] 210 4$d©2005 215 $a1 online resource (134 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 831 300 $a"Volume 176, number 831 (third of 5 numbers)." 311 $a0-8218-3716-8 320 $aIncludes bibliographical references (pages 111-113) and index. 327 $a""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 properties 327 $athe monoids Z[sub(I?³)], R[sub(I?³)], and 2[sub(I?³)]""""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 | I?±)""; ""3-6. The dimension function I??""; ""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"" 327 $a""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"" 327 $a""L""""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""X""; ""Z"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 831. 606 $aLattice theory 606 $aBoolean rings 606 $aPartial algebras 606 $aModules (Algebra) 615 0$aLattice theory. 615 0$aBoolean rings. 615 0$aPartial algebras. 615 0$aModules (Algebra) 676 $a510 s 676 $a511.3/3 700 $aGoodearl$b K. R.$057894 702 $aWehrung$b F$g(Friedrich),$f1961- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827772403321 996 $aThe complete dimension theory of partially ordered systems with equivalence and orthogonality$94049204 997 $aUNINA