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