INDEX 367 unique factorization domain, 14, 25, 26, 307, 338 unitary group U(n), 84, 151 unitary transformation, 84 universal bound, 57 universally catenary, 167, 170 unramified homomorphism, 321–328, 330 local homomorphism, 66, 67, 164, 164, 321–322, 325 prime ideal, 322, 325, 326, 330, 336, 337, 339 unramified in codimension one, 66, 67, 69, 118, 327, 328, 330, 339 V(R), 13 valued tree, 117 Vandermonde matrix, 244 Vasconcelos, Wolmer V., 44 Verdier, Jean-Louis, 97, 104, 160 Wakamatsu’s Lemma, 211, 213 Warfield, Robert B., 31 Watanabe, Kei-ichi, 81, 84, 98 weakly extended module, 43, 47, 59, 165–167, 171 weakly liftable module, 43 Wedderburn, J. H. M., 1 Wedderburn-Artin Theorem, 5, 6 Weierstrass Preparation Theorem, 142, 144, 300 Weierstrass, Karl, 31 Wiegand, Roger, 38, 50, 57 Wiegand, Sylvia, 57 Yoneda correspondence, 109, 110 Yoshino, Yuji, 114, 146, 188, 200, 268, 275, 276 Zariski and Samuel, 144 Zariski topology, 35, 102, 103 Zariski’s Main Theorem, 99
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