Abstract Algebra Theory and Applications - Computer Science ...

INDEX 419error-locator, 363greatest common divisor of, 263in n indeterminates, 260irreducible, 265leading coefficient of, 257minimal, 326minimal generator, 354monic, 257primitive, 288root of, 262separable, 369zero of, 262Polynomial separable, 347Posetdefinition of, 295largest element in, 299smallest element in, 299Power set, 32, 295Prime element, 282Prime field, 292Prime ideal, 244Prime integer, 29Prime subfield, 292Primitive nth root of unity, 64, 378Primitive element, 369Primitive Element Theorem, 369Primitive polynomial, 288Principal ideal, 241Principal ideal domain (PID), 283Principal series, 196Pseudoprime, 106Quaternions, 43, 235Repeated squares, 64Resolvent cubic equation, 275Right regular representation, 151Rigid motion, 38, 179RingArtinian, 293Boolean, 253center of, 254characteristic of, 238commutative, 233definition of, 232division, 233factor, 242finitely generated, 293homomorphism, 239isomorphism, 239local, 293Noetherian, 284of integers localized at p, 254of quotients, 293quotient, 242with identity, 233with unity, 233Rivest, R., 101RSA cryptosystem, 101Ruffini, P., 376Russell, Bertrand, 308Scalar product, 312Schreier’s Theorem, 201Second Isomorphism Theoremfor groups, 163for rings, 243Semidirect product, 187Shamir, A., 101Shannon, C., 117Sieve of Eratosthenes, 34Simple extension, 325Simple group, 158Simple root, 368Solvability by radicals, 378Spanning set, 315Splitting field, 334Squaring the circle, 341Standard decoding, 129Subfieldprime, 292Subgroupp-subgroup, 220centralizer, 207commutator, 168, 200, 225cyclic, 57definition of, 46index of, 91isotropy, 205normal, 152