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Fuch L. — Partially ordered algebraic systems

Fuch L. — Partially ordered algebraic systems

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Название: Partially ordered algebraic systems

Автор: Fuch L.

Аннотация:

Algebraic systems endowed with a partial or full order are; met with in several disciplines of mathematics. Because the; theory of partially ordered algebraic systems is extensive;' I have had to abandon the claim to completeness and to be — content with developing the main algebraic aspects of the theory. This is the reason why some important topics, such &s partially ordered linear or topological spaces, have not Ьеец. taken into consideration. Moreover, a certain limitation was* also necessary in the presentation of results which are purely: algebraic in character. To enable the reader to find out more, about the subject, references have been provided not only tp= the original sources of the material here collected, but also toz a number of important results which I have not been able to include. No attempt has been made to cover the whole vast: field of partially ordered algebraic systems in the bibliography,; but for the narrower field surveyed here, the bibliography, should be fairly complete. *i

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Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Добавлена в каталог: 04.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$O^\ast$ -group      39
$\alpha$ -cut      173
$\beta$ -cut      173
$\bigvee$ -groupoid, $\bigwedge$ -groupoid      153
$\bigvee$ -semilattice, $\bigwedge$ -semilattice      3
$\Phi$ -prime, $\Phi$ -primary, $\Phi$ -primal      195
$\upsilon$ -system      101
Absolute      44 74
Absolutely convex      210
Aczel, J.      182 186 188
Albert, A.A.      110 115 126 131
Algebraic structure      4
Algebraic system      4
Alimov, N.G.      161 162 163 167
Almost ordered group      10
Anomalous pair      162
Antisymmetry      1
Antitone      4
Archimedean      12 126 162 182
Archimedean classes      44 128 171
Archimedean complete      65
Archimedean equivalence      44 171
Archimedean extension      55
Artin, E.      117 119 120 121 192
atom      71
Autodistributive law      182
Baer, R.      33 46 94 117 129
Banaschewski, B.      60 99 127 129
Birkhoff, G.      viii 1 3 11 13 14 16 23 29 49 66 67 68 71 74 78 79 80 82 87 91 109 115 128 141 143 144 145 148 149 150 155 157 189 208 209 212
Bisymmetric law      182
Bounded      2
Bourbaki, N.      118
Britton, J.L.      10
Brown, B.      111
Bruck, R.H.      14 48 49
Burgess, D.C.J.      1
Busulini, B.      76
Cantor extension      96
Cardinal product      22
Carrier      72
Cartan, H.      46
Cernikov, S.N.      54
Certaine, J.      189
Chain      2
Chehata, C.G.      19 39 46 161
Clifford, A.H.      10 13 19 43 60 82 89 95 155 156 163 165 173 176 178 180 181
Closed      30 90
Closure operation      93
Closure operator      195
Cofinal      30
Cohen, L.W.      33 96
Cohn, P.M.      10 21 47
Complete l.o. group      89
Complete l.o. groupoid      191
Completely integrally closed      12
Conditional lattice      93
Conditionally complete      89
Conic semiring      106
Conrad, P.      viii 10 21 22 37 47 60 61 81 82 83 84 86 117 161 172 175
Convex      2
Convex subgroup      18
Croisot, R.      viii 157 191 192 193 204 205 208
Cut      58 173 181
Cyclically ordered      62
Dedekind extension      95
Diagonal l.o. group      97
Dickson, L.E.      115
Dieudonne, J.      43 117
Dilworth, R.P.      189 204
Direct product      22
Directed      3
Directed group      10
Directed ring      105
Disjoint      70
Division-closed      107
Domain of integrity      110
Dual      1
Dual isomorphism      2
Dubreil, P.      72 139 155 156 193 194
Dubreil-Jacotin, M.-L.      viii 72 157 191 192 193 208
Endpoint      1
Equationally definable      66
Equivalence of Artin      192
Erdoes, J.      60
Etherington, I.M.H.      182
Even product      117 123
Everett, C.J.      12 39 49 67 94 95 96 97 98
Extension of partial order      2
F-ring      143
f.o.=fully ordered      2
f.o.=fully ordered group      11
f.o.=fully ordered ring      105
f.o.=fully ordered semigroup      162
Fan, K.      47
Field      105
Filet      72
Finer ideal system      100
Formal power series      134
Formally real      117
Freudenthal, H.      87
Full order      2
Fully ordered set      2
Function ring      143
Fundamental sequence      96
g.l.b.      3
Generalized periodic      15
Gerbier      191
Goffman, C.      33 73 96 148
Graetzer, G.      110 210 212
Gravett, K.A.H.      60
Hahn, H.      25 55 59 60 137
Harvey, J.      60
Hausner, M.      57 60
Hilbert, D.      126 137
Hion, Ya.V.      46 126 130 156 170 171
Hoelder, O.      45 164 165
Holland, Ch.      60 133
Homogeneity law      9
Hosszu, M.      187
Huntington, E.V.      167
Immediate extension      55
Incomparable      1
Incomparably smaller      44
Induced order      1 18 20
Infinitely small      44
integral      12
Integral part      12
Integrally closed      193
Intersection      3
interval      1 2
Invariant carrier      74
Irredundant intersection      197
Iseki, K.      33 46
Isolated partial order      15
Isomorphism      2
Isotone      2 4
Iwasawa, K.      49 53 91
Jaeger, A.      140
Jaffard, P.      12 22 72 73 82 83 89 102
Jakubik, J.      24 88 89
Johnson, D.G.      111 132 133 146 147 149 150
Johnson, R.E.      117
Join      3
Jump      50
Kalman, J.A.      77
Kantorovitch, L.V.      74 78 90
Kerstan, J.      208
Klein-Barmen, F.      173
Klingenberg, W.      211
KontoroviC, P.G.      74

Krasner, M.      54
Krishnan, V.S.      178 181 208
Krull, W.      20 95 117 146 195
KuroS, A.G.      28 54
Kutyev, K.M.      70 74
l-directed      3
L-group      11
L-ideal      78
l-negative      154
l-positive      154
L-product      142
L-radical      149
l.o.=lattice-ordered group      11 66
l.o.=lattice-ordered groupoid      153 191
l.o.=lattice-ordered ring      105 141
l.o.=lattice-ordered vector group      88
l.u.b.      3
Lattice      3
Left-residual      189
Lesieur, L.      viii 157 191 192 204 205 208
Levi, F.W.      20 36 37 38 46
Lexicographic extension      20
Lexicographic extension, $\sigma$ -product      25
Linear closure operator      195
Linear order      2
Lines Escardo, E.      67
Loonstra, F.      22 33 45 47
Lorenz, K.      80 88
Lorenzen, P.      36 39 41 42 68 88 95 99
Los, J.      36
Lower bound      2
Lower semi-continuous      176
m-direct product      23
MacNeille, H.      93
Magnus, W.      49
Mal'cev, A.I.      25 26 28 40 53 138 161
Mallol Balmana, R.      67
Matsushita, S.      10 50
Maximally valued      55
McCoy, N.H.      111
Mean groupoid      182
Meet      3
Meet-irreducible      201
Michiura, T.      47 67
Minimal prime      202
Molinaro, I.      194
Monotony domain      5
Monotony law      5
Moore — Smith property      3
Moufang, R.      138
Murata, K.      208
Nakada, O.      154 161
Natural valuation      55 129
Naturally ordered groupoid      154
Negative      12 105 154
Negative cone      157
Negative part      74
Negatively ordered groupoid      154
Neumann, B.H.      viii 19 35 36 37 38 48 49 110 137 138 140 210 211
Nilpotent L-ideal      148
Non-degenerate operation      5
Normal completion      178
o-automorphism      21
o-complete      96
o-convergent      29
o-epimorphism      21
O-group      35
o-homomorphism      20
o-ideal      20
o-isomorphism      21
o-limit      29
O-ring      114
o-simple group      19
o-simple group ring      132
Ogasawara, T.      91
Ohnishi, M.      36 39
Open-interval topology      33
Operator      195
Operator group      12
Order topology      29
Order-convergence      29
Order-convergence-isomorphism etc.      2 21
Order-preserving      2
Ordinal sum      173
Ordinally irreducible      173
Ore, O.      110
Orthogonal      70 81
p.o.=partially ordered      1
p.o.=partially ordered algebraic system      5
p.o.=partially ordered group      9
p.o.=partially ordered groupoid      153
p.o.=partially ordered ring      105
p.o.=partially ordered semigroup      153
Partial order      1
Partially ordered set      1
Pickert, G.      46 117 126 127
Pierce, R.S.      73 79 109 115 141 143 144 145 147 148 149 150
Podderyugin, V.D.      40 51 114 117
Positive      12 105 154
Positive cone      12 105 157
Positive part      74
Positively ordered groupoid      154
Preorder      1 10
Primal      196
Primary      196
Prime      195
Prime L-ideal      146
Principal automorphism      52
Principal l-ideal      78
Pruefer, H.      99
Quasiorder      1
r-ideal      100
r-ideal system      100
r-negative      154
r-positive      154
Radical      202
Real closed      119
Real group      53
Redei, L.      viii 111
Reduced intersection      197
Refiexivity      1
Regular l.o. group      88
Residuated p.o. groupoid      189
Ribenboim, P.      55 60 73
Rieger, L.S.      19 22 46 51 62 64
Riesz, F.      68 74 78 90 91
Right $\Phi$ -primal      196
Right-residual      189
Right-residuated groupoid      189
Ring      105
Ring of quotients      109
s-system      100
Sade, A.      182
Schilling, O.F.G.      46
Schmidt, E.T.      110
Schreier, O.      117 119 120 121
Secondary radical      204
Semi-prime      202
Semi-simple ring      115
Semigroup of quotients      160
Serre, J.-P.      117 118
Shepperd, J.A.H.      10 37 65
Short decomposition      198
Sik, F.      35 80 88 89
Simbireva, E.P.      20 22 23 37 39 42 43 48
Simple order      2
Skeleton      55
Steinfeld, O.      208
Stelleckii, I.V.      208
Stone, M.H.      66

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