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Biquadratic field

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218: 244: 249: 206: 39: 119: 107: 214: 184: 192: 50: 35: 228: 224: 130: 213:, London Mathematical Society Student Texts, vol. 50, Cambridge University Press, 238: 126: 46: 28: 62: 20: 138: 141:
of index 2. The third subfield, to add to the evident
61:
Biquadratic fields are all obtained by adjoining two
65:. Therefore in explicit terms they have the form 183:Biquadratic fields are the simplest examples of 8: 211:A brief guide to algebraic number theory 7: 137:, since the Galois group has three 14: 34:of a particular kind, which is a 1: 266: 245:Algebraic number theory 207:Swinnerton-Dyer, H.P.F. 57:Structure and subfields 16:Algebraic number theory 129:, there must be three 98:for rational numbers 40:rational number field 120:square-free integers 118:to be non-zero and 185:abelian extensions 108:loss of generality 220:978-0-521-00423-7 193:cyclic extensions 25:biquadratic field 257: 231: 179: 178: 166: 165: 153: 152: 131:quadratic fields 93: 92: 84: 83: 51:Klein four-group 36:Galois extension 265: 264: 260: 259: 258: 256: 255: 254: 235: 234: 221: 205: 201: 174: 172: 161: 159: 148: 146: 88: 86: 79: 77: 59: 17: 12: 11: 5: 263: 261: 253: 252: 247: 237: 236: 233: 232: 219: 204:Section 12 of 200: 197: 106:. There is no 96: 95: 58: 55: 15: 13: 10: 9: 6: 4: 3: 2: 262: 251: 250:Galois theory 248: 246: 243: 242: 240: 230: 226: 222: 216: 212: 208: 203: 202: 198: 196: 194: 191:that are not 190: 186: 181: 177: 170: 164: 157: 151: 144: 140: 136: 133:contained in 132: 128: 127:Galois theory 125:According to 123: 121: 117: 113: 109: 105: 101: 91: 82: 75: 71: 68: 67: 66: 64: 56: 54: 52: 48: 44: 41: 37: 33: 30: 26: 22: 210: 188: 182: 175: 168: 162: 155: 149: 142: 134: 124: 115: 111: 103: 99: 97: 89: 80: 73: 69: 63:square roots 60: 47:Galois group 42: 31: 29:number field 24: 18: 21:mathematics 239:Categories 199:References 110:in taking 139:subgroups 209:(2001), 229:1826558 173:√ 160:√ 147:√ 87:√ 78:√ 38:of the 227:  217:  167:), is 154:) and 45:with 27:is a 215:ISBN 180:). 114:and 102:and 49:the 23:, a 187:of 122:. 19:In 241:: 225:MR 223:, 195:. 176:ab 72:= 53:. 189:Q 171:( 169:Q 163:b 158:( 156:Q 150:a 145:( 143:Q 135:K 116:b 112:a 104:b 100:a 94:) 90:b 85:, 81:a 76:( 74:Q 70:K 43:Q 32:K

Index

mathematics
number field
Galois extension
rational number field
Galois group
Klein four-group
square roots
loss of generality
square-free integers
Galois theory
quadratic fields
subgroups
abelian extensions
cyclic extensions
Swinnerton-Dyer, H.P.F.
ISBN
978-0-521-00423-7
MR
1826558
Categories
Algebraic number theory
Galois theory

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