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Primary extension

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189: 230: 165: 223: 254: 216: 17: 249: 156:. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11 (3rd revised ed.). 94: 204: 175: 8: 44: 161: 112: 101: 73: 69: 196: 171: 157: 32: 200: 243: 108: 90:
A primary extension of a primary extension is primary (transitivity).
188: 87:A subextension of a primary extension is primary. 241: 224: 151: 104:if and only if it is separable and primary. 231: 217: 152:Fried, Michael D.; Jarden, Moshe (2008). 242: 139: 137: 135: 133: 131: 129: 183: 126: 35:such that the algebraic closure of 13: 14: 266: 187: 68:is primary if and only if it is 143:Fried & Jarden (2008) p.44 1: 119: 54: 203:. You can help Knowledge by 7: 10: 271: 182: 107:A primary extension of a 20:, a branch of algebra, a 255:Abstract algebra stubs 199:-related article is a 95:separably closed field 93:Any extension of a 160:. pp. 38–44. 45:purely inseparable 212: 211: 167:978-3-540-77269-9 74:separable closure 70:linearly disjoint 22:primary extension 262: 250:Field extensions 233: 226: 219: 197:abstract algebra 191: 184: 179: 154:Field arithmetic 144: 141: 100:An extension is 270: 269: 265: 264: 263: 261: 260: 259: 240: 239: 238: 237: 168: 158:Springer-Verlag 148: 147: 142: 127: 122: 57: 33:field extension 12: 11: 5: 268: 258: 257: 252: 236: 235: 228: 221: 213: 210: 209: 192: 181: 180: 166: 146: 145: 124: 123: 121: 118: 117: 116: 105: 98: 91: 88: 85: 56: 53: 9: 6: 4: 3: 2: 267: 256: 253: 251: 248: 247: 245: 234: 229: 227: 222: 220: 215: 214: 208: 206: 202: 198: 193: 190: 186: 185: 177: 173: 169: 163: 159: 155: 150: 149: 140: 138: 136: 134: 132: 130: 125: 114: 110: 109:perfect field 106: 103: 99: 96: 92: 89: 86: 83: 79: 75: 71: 67: 63: 60:An extension 59: 58: 52: 50: 46: 42: 38: 34: 30: 26: 23: 19: 205:expanding it 194: 153: 81: 77: 65: 61: 48: 40: 36: 28: 24: 21: 18:field theory 15: 97:is primary. 244:Categories 176:1145.12001 120:References 55:Properties 72:from the 113:regular 102:regular 174:  164:  195:This 80:over 47:over 31:is a 201:stub 162:ISBN 172:Zbl 111:is 76:of 43:is 39:in 27:of 16:In 246:: 170:. 128:^ 51:. 232:e 225:t 218:v 207:. 178:. 115:. 84:. 82:K 78:K 66:K 64:/ 62:L 49:K 41:L 37:K 29:K 25:L

Index

field theory
field extension
purely inseparable
linearly disjoint
separable closure
separably closed field
regular
perfect field
regular






Springer-Verlag
ISBN
978-3-540-77269-9
Zbl
1145.12001
Stub icon
abstract algebra
stub
expanding it
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t
e
Categories
Field extensions
Abstract algebra stubs

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