Abstract Algebra Theory and Applications - Computer Science ...

IndexG-equivalent, 205G-set, 203nth root of unity, 63, 378Abel, Niels Henrik, 376Abelian group, 41Ackermann’s function, 34Adleman, L., 101Algebraic closure, 332Algebraic extension, 325Algebraic number, 325Algorithmdivision, 261Euclidean, 29Artin, Emil, 293Ascending chain condition, 284Associate elements, 282Atom, 302Automorphisminner, 151, 168of a group, 150Basis of a lattice, 182Bieberbach, L., 186Binary operation, 40Binary symmetric channel, 112Boole, George, 307Boolean algebraatom in a, 302definition of, 300finite, 302isomorphism, 302Boolean function, 214, 311Boolean ring, 253Burnside’s Counting Theorem, 210Burnside, William, 46, 161, 216Cancellation lawfor groups, 45for integral domains, 238Cardano, Gerolamo, 271Carmichael numbers, 107Cauchy’s Theorem, 220Cauchy, Augustin-Louis, 81Cayley table, 41Cayley’s Theorem, 142Cayley, Arthur, 143Centerof a group, 52of a ring, 254Centralizerof a subgroup, 207of an element, 167Characteristic of a ring, 238Chinese Remainder Theoremfor integers, 247for rings, 254Cipher, 97Ciphertext, 97Circuitparallel, 305series, 305series-parallel, 306Class equation, 207CodeBCH, 359414