Index
Abel N. 274
abelian group 11,19, 37,90-93, 139, 314
characters of 229
abelian X-group 142-153,156,157,167
ACC (ascending chain condition) 143-145,
433
action
of group 42-43
oncosets 44,45, 115
via automorphisms 95, 112,114
adjectives 163
adjoint matrix 439,456
affine group of line 8,29
afforded character 216
algebra (over a field) 166,171,172,173,213,
295
algebraic closure 267-268,271
of finite degree 401^07,415
algebraic element 254-259, 386, 398
algebraic field extension, definition of 256
algebraic geometry 493
algebraic integer 454,463,469,471-472
algebraic number 256
algebraic number field 256
algebraic numbers, field of 256, 259,268,
410
algebraic point 494
algebraic set 493-505
algebraically closed field 267-269, 303, 355
algebraically independent elements 379-380,
383, 398
alternating group 75
simplicity of 77
annihilator {see also prime annihilator) 163,
176,177,210-211,440,442
antichain 157
archimedian ordered field 412-413
Artin, E. 145-146
Artin-Rees theorem 461
Artin-Schreier theorem 401
Artin's theorem 260, 262, 389
artinian module 170,444
artinian ring {see right artinian ring or
left artinian ring)
artinian commutative ring 252,428
artinian X-group 145-146,148-149,150,
157
ascending central series {see upper central
series)
ascending chain condition {see ACC)
associated factors 338
associated prime ideal 440-442,450
associative property 9
augmentation ideal 173
augmentation map 173
automorphism
of group 19-22
of symmetric group 79-80
automorphism group
of algebraically closed field 405
of group 20,28,41,310
axiom of choice 5, 144-145,153, 269
basis for free module 202, 434
Berlekamp algorithm 333-339,464
bijection 4
binary operation 9
507
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