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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