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von Neumann J. — Continuous Geometry
von Neumann J. — Continuous Geometry

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Название: Continuous Geometry

Автор: von Neumann J.

Аннотация:

In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry.

This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and — for the irreducible case — the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 316

Добавлена в каталог: 23.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition of L-number      136 144
Addition of L-numbers      136 144
Additivity of dimension      54
Additivity of dimension function      54
Amemiya, I.      283 284 285 288 290 291
Anti-automorphism      77 112 113 114
Anti-isomorphic      71
Associative      132
Associative addition      144
Atomistic      256 261
Automorphism      104
Auxiliary ring      160 168 201
Axis      16 19
Baer ring      285 295
Basis      93
Berberian, S. K.      286
Binary relation      32
Birkhoff, G.      3 58 133 254 283 292
Boolean algebra      8 13 34 76 77 240 245 251 255 256
Brown, B.      286
CASE      58
Case I      182 190 191 196 208
Case II      182 190 197 199 208
Center      73 230 261
Center of continuous geometry, Z      240
Central envelope      242
Chain condition      68 82 83 84
Commutative addition      144
Comparability      36
Complementation      2
Complemented lattice      68 73
Complete metric space      228
Continuity of lattice      1
Continuity of lattice operations      2
Continuous Boolean algebra      242
Continuous geometry, L$_{\infty}$      63 66 222
Continuous lattice      65 246
Continuous ring      222 231
coordinates      63
Decomposibility      259
Decomposition      259
Dedekind      3 283
Dimension function      58 59 83 222
Direct sum      33 74
Direct sum decomposition      259
Discrete element      278
Discrete geometry      133
Discrete ring      222
Distributive      32
Distributive lattice      240 246
Distributive laws      77 151 262
Distributive multiplication      154
Distributive relation      32
Division algebra (or field)      65
Dual      64
Dual automorphism      112 113 114
Dual theorem      3
Duality      3
Equivalence class      264
Factor      88 209
Factor isomorphism      220
Factor-correspondence      209
Field      65
First category      255
Frame      118
Frink, O.      295
Fryer, K. D.      285 288 289 290 291
Funayama, N.      283
Fundamental sequence      228
Greatest lower bound      1
Groupoid      211
Halperin, I.      283 284 285 288 289 290 291 294 295
Hausdorff, F.      228 254
Hermitian      85 113
Hilbert space      85 283 295
Homogeneous      93
Homogeneous basis      93 135
Hypercomplex system      85
Ideal      63 65 250 251
Idempotent elements      69 70
Idempotent matrix      81
Independence      8 9 10 11
Independent      93
Independent sequence      24 29 30 55
Inner automorphism      214 217
Inner isomorphism      214 298
Intersection      65
Inverse element      3 5 6 7 24 29 30 31 33 214
Inverse ideal      69
Inverse transformation      71
Involutoric      114
Irreducible      33 38 39 75 88 89
Irreducible lattice      3 6
Irreducible ring      230
Isomorphic lattices      16 18
Isomorphism theorems      103
Iwamura, T.      294 295
Join      65
Jonsson, B.      288
Kaplansky, I.      283 284 285
Kummerian ideal-theory      68
Kuratowski, C.      228
L$\ddot{o}$wig, H.      291
L-number      130
Lattice automorphism      217 220
Lattice isomorphism      103 108 112 211
Lattice polynomial      105
Lattice, L      3 64
Least upper bound      1 2 5 8
Lebesque measure      253 257
Left ideal      65
Left ratio      64
Lim      2
Linear equation      78
Lipschitz condition      232
Loomis, L. H.      295
MacNeille, H. M.      3 283
Maeda, F.      292 293 294
Maeda, S.      295
Matrices      65
Matrix ring      67 90
Matrix space      227
Matrix units      97
Maximal element      37 38
McCoy, N. H.      286
Menger, K.      58
Minimal      86
Minimal element      48 86 277
Minimal sequence      48
Minimum-maximum condition      82
Modular lattice      73
Modularity      2
Moore, E. H.      84
Moufang      288
Multiplication of L-number      132
Multiplication of L-numbers      132
Murray, F. J.      85 285 286 295
Nilpotent      83
Non-Desarguesian plane geometry      103
Non-singular      214
Normalized      118
Normalized frame      118 178 201
Nowhere dense      255
Operator      85
Order of a basis      93
Order of a lattice      93
Partially ordered set      3
Permissible triple      136
Perspective      16 17 18
Perspective by decomposition      24
Perspective isomorphism      16 19 21 26 27 119 191
Principal right ideal      66 67 68 69 95
Projection      85
Projective      19
Projective automorphism      191 194 195 220
Projective geometry, L$_{n}$      3 63 67 222
Projective isomorphism      19 117 130 131
Radical      83
Range of the dimension      56
Rank      224
Rank function      231
Rank metric      231
Reducible      33 38 39
Regular ring      69 70 90 93
Relation      96
Right ideal      65
Right linear      64 81
Right ratio      63
Ring      64
Ring automorphism      220
Ring isomorphism      103 108 112
Ring of L-number      157
Ring of-L-numbers      154
Ring, rank      231
Schmidt, E.      89
Self-dual      32 42
Semi-isomorphism      158
Semi-simple      116
Semi-simplicity      68 70 83 85 116
SIMPLE      88 89
simplicity      88
Special factors      209
Statement (*)      184 196
Statement (**)      186 191 196 197 199
Stone, M. H.      87 245
Strongly less than      266
Strongly minimal      82
Subtraction of L-number      154
Subtraction of X-numbers      154
Tarski, A.      256 257 261
Ternary relation      32
topology      228
Totally continuous operator      89
Transitive      41
Transitivity of perspectivity      104 264
Unary relation      32
van der Waerden, B. L.      64 82 84 85
Veblen, O. and Young, J. W.      63 135. 149 150 158
von Neumann, J.      85 87 254 283 284 285 287 291 292 293 294 295
Von Staudt      135 136
Weakly minimal      82
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