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Faith C. — Rings and Things and a Fine Array of Twentieth Century Associative Algebra
Faith C. — Rings and Things and a Fine Array of Twentieth Century Associative Algebra

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Название: Rings and Things and a Fine Array of Twentieth Century Associative Algebra

Автор: Faith C.

Аннотация:

A survey of aspects of the development of associative rings and modules in the twentieth century including: (1) updates on topics treated in the author's two Springer-Verlag Grundlehren (Foundations) volumes written a quarter of a century ago, (2) a considerable expansion of topics to include exciting new ideas that drive and dominate contemporary research. The title of this book is derived from The Taming of the Shrew.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 449

Добавлена в каталог: 29.10.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"Alice-in-Wonderland"      278
"Captain" Bill      318
"Chicago Seven"      321
"Crazy Eddie"      318
"Hagar The Horrible"      301
"Illiac"      281
"Maniac"      280
"Midnight"      276
"Tiger" (Walker)      281
"Tinkers to Evens to Chance"      303
"Tokyo Rose"      306
"Undergraduate Gems at Rutgers"      321—322
"Zebra"      276
$f\cdot g$      see "Finitely generated"
$f\cdot g$-injective module      4.2Bs 6.Es
$\aleph_0$-injective      4.2Bs
$\Delta$-injective      3.10A 7.45s
$\mathcal{E}_{max}, \mathcal{E}_{min}$ ring      6.38(4) 16.39s
$\perp$acc (= acc on annihilator left ideals)      1.24A
$\Pi$-quasi-injective module      3.9
$\pi$-regular ring      8.4Fs
$\Sigma$-cyclic      5.1As
$\Sigma$-injective module      3.7As 3.14—3.16 7.33—7.34
$\Sigma$-pure-injective module      6.55s
$\Sigma(\Delta)$-ring      7.47s
$\sqrt{acc}$ on radical ideals      14.34s
$\varphi$-differential      7.14f
(Strongly) invariant coefficient ring      10.1s
Abelian idempotent      4.3As
Abelian von Neumann regular ring (=VNR)      4.3As
Abelian — von Neumann regular ring      4.3As
Abhyankar — Heinzer — Eakin Theorem      10.5
Absolute value      1.30ff
ACC      see "Ascending chain condition"
Acc on radical ideals      14.34—14.38
acc$\oplus$ = acc on direct sums      3.13s
acc$\perp$ (= acc on annihilator right ideals)      1.24A
acci (= acc on irreducible ideals)      16.35s
accra (= acc on right annihilator ideals)      2.37G
accsi (= acc on subdirectly irreducible ideals)      16.35s
Adkins, Theodore      255
Affine algebra      14.46
Affine ring (= $f\cdot g$ ring)      2.21Bs 2.21Bf
Ahsan theorem      12.4C'f
Akasaki theorem      3.29
Akiba theorem      9.24(3)
Al-Huzali — Jain — Lopez-Permouth theorem      6.37
Alamelu theorem      12.23—12.24
Albert      48
Albert theorem      2.50f
Albert, Adrian A.      258—259 286
Albrecht theorem      3.23A—3.23B
Albu      194 211
Albu — Nastasescu theorem      3.33D
Aldosray      44
Algebra Seminar ("World's Greatest")      313
Algebra, affine      14.46
Algebra, algebraic      1.28As
Algebra, free      15.14s 15.14ff
Algebra, polynomial identity (= PI)      15.1s 15.14s
Algebra, separable      14.15Bs
Algebra, split-split      4.15B
Algebraic algebra      1.28As 15.1(7)
Algebraic bounded degree      15.1(7) 15.12
Algebraic function field      1.28As
Algebraic number field      1.28C(2)
Algebraic, absolutely      1.28As 2.40s
Algebraic, matrix      2.6Bs
Algebraically closed field      1.28Bs
Algebraically compact      1.25s 6.Af
Algebraically compact module      1.25s 6.Af
Alliluyeva, Svetlana      271 318
Almost maximal ring      5.4Bs 5.16
Almost maximal valuation ring      5.4D 5.52s
Amdal — Ringdal theorem      5.2C
Amitsur      19 24 36 72 144 176
Amitsur theorem      2.6C 2.40 2.49 3.43—3.49 15.14
Amitsur — Kaplansky Theorem      15.4
Amitsur — Levitzki theorem      15.2
Amitsur — Small Theorem      3.36D 15.17
Amitsur, Shimshon      288—289 304
Anarin      30
Anarin — Zjabko theorem      2.16Cf
Anderson      137 168
Anderson — Fuller theorem      8.6 8.8
Anderson, Frank W.      281
Anh      108 111 127 197
Anh theorem      13.6
Annie Page theorem      9.26E
Annihilator, chain conditions on      3.7A—3.7B 16.19
Annihilator, double condition      3.8
Annihilator, maximal      2.33Es
Annihilator, right ideal      2.16F 2.37Es
Annulet      2.37Es 16.30s
Ara, Pere      309
Arena — Kaplansky theorem      4.19A
Arens      94
Arens — Kaplansky Theorem      4.19A
Arhangel’skii      77 193
Arithmetic ring      6.4
Armendariz      181
Armendariz theorem      6.4
Armendariz — Steinberg Theorem      4.5 4.18
Armstrong, Neil      302
Artin — Schreier theorem      1.30ff
Artin — Tate      3.8s
Artin — Tate Theorem      3.8s
Artin — Wedderburn theorem      2.1ff
Artin, E.      13 21 23 49 57 243
Artin, E. conjecture      2.6ff
Artin, E. problem      2.7s
Artin, E. question      2.7s
Artin, Emil      315 315n 316 319
Artin, Karin      315
Artin, M.      99
Artin, M. theorem      4.14s
Artin, Michael ("Mike")      315 316
Artin, Nataly Jasny      315
Artin, Thomas      315
Artinian modules      2.17As
Artinian rings      2.1f
Asano      151
Asano criterion      5.1A
Asano theorem      5.1A
Ascending chain condition (acc) on right annihilators (acc$\perp$)      1.24A
Ascending chain condition (acc) on right ideals      2.2s
Ascending chain condition (acc) on submodules      2.17As
Ascending Loewy chain      3.33As
Asensio      135
Ashbacher, Michael      301
Ass(M), Ass*(M)      16.11 16.17
Atkins      245
Attenborough, Sir Richard      295
Auslander      99 160—161 243 253
Auslander theorem      4.1A 11.9 14.11—14.12 14.15.1
Auslander — Buchsbaum theorem      14.16
Auslander — Goldman theorem      4.13f
Auslander, Maurice ("Moe")      299 315
Automorphism definition      2.5As
Automorphism group      2.7s see
Automorphism group, cleft      17.13As
Automorphism group, dependent      17.0s 17.9ff
Automorphism group, independence theorem      17.0
Automorphism group, quorite      17.9s
Automorphism, inner      2.5A
Ayoub, C. theorem      1.26A
Azumaya      24 49 71 114 157 194
Azumaya algebra      4.13
Azumaya diagram      8.As
Azumaya theorem      4.15 4.20 13.7
Azumaya — Krull — Schmidt unique decomposition theorem      8As
Babai, L.      290n
Baer      5 45 52 196
Baer criterion      3.2C
Baer lower nil radical      2.38A
Baer theorem      1.18 3.2
Baer, Reinhold      263 284 299 315
Baire category theorem      16.6
Balanced module      3.50Bf 13.29s 13.30As
Balanced rings      13.29s
Balcerzyk theorem      1.19A 1.20A
Ballet theorem      13.11A
Bamberger, Louis      273 278
Barr, Patricia ("Patty")      258
Barrow, John D.      256
Basic indempotent      3.53
Basic module      3.53
Basic ring      3.52
Basis number      1.1 3.63
Basis, countable      1.1
Basis, finite      1.1
Basis, free      1.1
Basis, normal      17.1s
Basis, transcendence      1.28
Bass      61 69 87—88 99 124 215
Bass theorem      2.24 3.4B 3.24A 3.26—3.27 3.30—3.32 3.33C 13.21
Bass, Hyman ("Hy")      287 305
Baxter      48
Beachy      80 102 181
Beachy theorem      3.58—3.61 7.9
Beachy — Blair      6.32A
Beachy — Kamil theorem      3.60
Beck theorem      3.15 3.16 3.28 16.33
Beck — Trosborg theorem      3.79
Becket, Samuel      282
Begin, Menachem      288
Bell      135
Berberian, Sterling ("Sam")      261
Bergman      20 130
Bergman theorem      6.33f 9.26A
Bergman, George      291
Berman      88
Bernstein, Felix      284
Bezout Domain      7.5Bs
Bezout ring      7.5Bs
Bialnicki theorem      1.21 A
Bigelow, Julian      280
Birkenmeier      94 104
Birkhoff      33 240
Birkhoff theorem      2.17C
Birkhoff, Garrett D.      255 291
Birula theorem      1.21A
Bishop, Errett      276
Bjoerk      87 143 184 200 209
Bjoerk theorem      3.5F 3.32f
Blair theorem      6.32A
Blair, Robert ("Bob")      261
Blassenohl, D.      256
Bloustein, Edward J.      302
Blumenthal      23
Bochner, Solomon      317
Bokut’      132
Bollabas, B.      290n
Bonic, Robert ("Bob")      316—317
Boole      33
Borel      87
Borel, Armand      267—268 270—271 312
Borel, Gaby      270—271
Borho      218
Bounded generator (BG)      8.8ff
Bounded order      1.8 1.14
Bounded ring      5.44Bs 15.17s
Bounded, strongly      5.44s
Bourbaki      85
Bourbaki — Lambek theorem      4.B
Bourbaki, N.      265 313 316
Bowtell      132
Boyle      172
Boyle conjecture      3.9C
Boyle theorem      3.9B 3.18B
Boyle, Ann Koski      286—287
Brandal      111
Brandal theorem      5.6
Brandeis      299
Brando, Marlon      295
Brauer      19 68 78 160 177
Brauer group      2.5Bff 4.16As
Brauer — Auslander — Goldman-group      4.15Af
Brauer — Hasse — Noether theorem      2.5Bff
Brauer, Richard      291 301
Bredon, Glen      299
Brewer      35 72 127 245
Brewer — Rutter Theorem      10.2—10.4
Brewer — Rutter — Watkins      6.12
Brodskii theorem      3.77—3.78
Bronowski, Jacob      300
Browder, Bill      316
Brown      49 94 211
Brown, Karen      299 315
Brown, Mort      275—276
Bruns      205
Buchsbaum, David      299 315
Bumby — Osofsky Theorem      3.3
Bumby, Dick      283—284
Burch      230
Burgess      48
Burnside      18
Burnside theorem      2.4
Busque — Herbera Theorem      4.17A
Busque, Claudi      309
Caesar, Julius      311
Cahen      167
Cailleau      64
Cailleau theorem      3.14
Calaprice, Alice      311n
Caldwell      161
Caldwell, Bill      283
Camillo      70 77—78 141 157 168 242 254
Camillo remarks (letters)      §17 Notes
Camillo theorem      1.23 3.33F H 3.51' 4.1B 5.20B 6.60—6.61 13.29 13.30E 16.51
Camillo — Fuller Theorem      4.26 13.30 13.30D
Camillo — Guralnick theorem      9.3
Camillo, Barbara      271
Camillo, Vic      271 286—287 312 319
Camps      124 159—160
Camps — Dicks Theorem      8.D
Camps — Menal Theorem      8.8ff
Camps, Rosa      269 308—309
Camus, Albert      317
Cancellation module      6.3Ds
Cancellation property      6.3Ds
Cancellation, matrix      10.8f (see p.174)
Cantor — Bernstein theorem      3.3
Capson      230
Carleson, Lennart      269
Carr, Raymond      311n
Cartan      52 206
Cartan theorem      2.6 2.7 3.4
Cartan — Brauer — Hua Theorem      2.15As
Cartan — Jacobson Theorem      2.7
Cartan, Henri      262—263
Castellet, Manuel      308
Castelnuovo theorem      1.31A
Cateforis — Sandomierski theorem      4.1E
Category mod-R      3.51s
Category of right R-modules      3.51s
Cauchon      71
Cauchon theorem      3.34A(1)
Cayley      15 21 see
Cedo      133 159 164
1 2 3 4 5 6 7 8
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