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Artin–Zorn theorem

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Finite fields and applications: proceedings of the Fifth International Conference on Finite Fields and Applications Fq5, held at the University of Augsburg, Germany, August 2–6, 1999
249: 189: 161: 128: 242: 268: 273: 235: 50:, which states that finite associative division rings are fields. As a geometric consequence, every finite 36: 223: 43:. It was first published in 1930 by Zorn, but in his publication Zorn credited it to Artin. 138: 8: 116: 93: 47: 185: 157: 124: 112: 97: 215: 85: 177: 134: 219: 262: 51: 40: 20: 89: 28: 207: 111:
Lüneburg, Heinz (2001), "On the early history of Galois fields", in
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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
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Points and Lines: Characterizing the Classical Geometries
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is the classical projective plane over a finite field.
46:The Artin–Zorn theorem is a generalization of the 260: 156:, Universitext, Springer-Verlag, p. 123, 243: 184:, Universitext, Springer-Verlag, p. 34, 250: 236: 74:(1930), "Theorie der alternativen Ringe", 176: 110: 261: 151: 123:, Springer-Verlag, pp. 341–355, 202: 70: 13: 14: 285: 206: 170: 145: 104: 64: 1: 57: 222:. You can help Knowledge by 7: 10: 290: 201: 182:A taste of Jordan algebras 37:alternative division ring 35:, states that any finite 269:Theorems in ring theory 274:Abstract algebra stubs 218:-related article is a 152:Shult, Ernest (2011), 117:Niederreiter, Harald 16:Mathematical result 113:Jungnickel, Dieter 90:10.1007/BF02940993 48:Wedderburn theorem 25:Artin–Zorn theorem 231: 230: 191:978-0-387-95447-9 163:978-3-642-15626-7 130:978-3-540-41109-3 39:is necessarily a 281: 252: 245: 238: 216:abstract algebra 210: 203: 196: 194: 178:McCrimmon, Kevin 174: 168: 166: 149: 143: 141: 108: 102: 100: 68: 289: 288: 284: 283: 282: 280: 279: 278: 259: 258: 257: 256: 200: 199: 192: 175: 171: 164: 150: 146: 131: 109: 105: 69: 65: 60: 17: 12: 11: 5: 287: 277: 276: 271: 255: 254: 247: 240: 232: 229: 228: 211: 198: 197: 190: 169: 162: 144: 129: 103: 62: 61: 59: 56: 27:, named after 15: 9: 6: 4: 3: 2: 286: 275: 272: 270: 267: 266: 264: 253: 248: 246: 241: 239: 234: 233: 227: 225: 221: 217: 212: 209: 205: 204: 193: 187: 183: 179: 173: 165: 159: 155: 148: 140: 136: 132: 126: 122: 118: 114: 107: 99: 95: 91: 87: 83: 79: 78: 73: 67: 63: 55: 53: 52:Moufang plane 49: 44: 42: 38: 34: 30: 26: 22: 224:expanding it 213: 181: 172: 153: 147: 120: 106: 81: 75: 66: 45: 41:finite field 24: 18: 84:: 123–147, 21:mathematics 263:Categories 58:References 29:Emil Artin 98:121384721 180:(2004), 119:(eds.), 72:Zorn, M. 33:Max Zorn 139:1849100 188:  160:  137:  127:  96:  23:, the 214:This 94:S2CID 220:stub 186:ISBN 158:ISBN 125:ISBN 31:and 86:doi 19:In 265:: 135:MR 133:, 115:; 92:, 80:, 251:e 244:t 237:v 226:. 195:. 167:. 142:. 101:. 88:: 82:8

Index

mathematics
Emil Artin
Max Zorn
alternative division ring
finite field
Wedderburn theorem
Moufang plane
Zorn, M.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
doi
10.1007/BF02940993
S2CID
121384721
Jungnickel, Dieter
Niederreiter, Harald
ISBN
978-3-540-41109-3
MR
1849100
ISBN
978-3-642-15626-7
McCrimmon, Kevin
ISBN
978-0-387-95447-9
Stub icon
abstract algebra
stub
expanding it
v
t

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