Index 1003 Papp, Z., 466 parallelogram law, 134 parity, 12 partially ordered set, 199 chain, 317 directed set, 506 discrete, 499 well-ordered, 318 partition, 34 partition of n, 242 path connected, 753 perfect field, 343 periodic cohomology, 837 permutation, 5 complete factorization, 9 cycle, 6 disjoint, 6 even, 12 odd, 12, 13 parity, 12 signum, 13 transposition, 6 permutation matrix, 564 PI-algebra, 714 PID, 127 Pigeonhole Principle, 15, 147 Poincar´ e, H., 753 pointwise operations, 85 P´ olya, G., 80 polynomial, 91 n variables, 94 associated reduced polynomial, 213 commuting variables, 713 cyclotomic, 119 function, 349 general, 166 irreducible, 107 monic, 93 noncommuting variables, 711 separable, 176 skew, 392 zero, 91 polynomial function, 93, 349 polynomial identity, 714 Pontrjagin duality, 468 positive definite, 691 power series, 91, 974 powers, 20 pre-additive category, 422 Premet, A., 748 presentation group, 280 module, 452 preserves finite direct sums, 616 multiplications, 801 presheaf, 513 primary component, 230, 641 Primary Decomposition abelian groups, 230 commutative rings, 363, 941 irredundant, 364 normal, 366 primary ideal, 361 belongs to prime ideal, 362 Prime Avoidance, 967 prime factorization, 112 prime field, 157 prime ideal, 296 associated, 364 belongs to primary ideal, 362 minimal, 321 minimal over ideal, 366, 963 primitive element, 106 theorem, 204 polynomial, 306 associated, 308 ring, 561 root of unity, 119 principal kG-module, 540 character (see trivial character), 570 derivation, 776 ideal, 100 ideal domain, 127 Principal Ideal Theorem, 963 product categorical family of objects, 429 two objects, 426 direct groups, 54 modules, 427 rings, 392 profinite completion, 502 profinite group, 521 projections direct sum, 224, 226 direct sum of modules, 408 product, 426, 429 projective dimension, 945 limit (see inverse limit), 500 module, 453 object in additive category, 618 plane, 749 resolution, 782 projective unimodular group, 265 projectively equivalent, 947 proper class, 419 divisor, 304 ideal, 99

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