Knowledge

Lattice (module)

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263: 201: 348: 107: 340: 375: 29: 358: 8: 45: 73: 33: 344: 354: 294: 274: 185: 69: 49: 369: 332: 41: 53: 21: 17: 339:. London Mathematical Society Monographs. New Series. Vol. 28. 84: 37: 258:{\displaystyle N\mapsto W=K\cdot N;\quad W\mapsto N=W\cap M.\,} 168:-torsion-free. There is a one-to-one correspondence between 204: 257: 48:, giving an algebraic generalisation of the way a 367: 297:is used to describe the lattice structure 254: 368: 331: 59: 285:-module embedded in a vector space 135: 13: 14: 387: 289:over the field of real numbers 229: 152:that is itself a lattice is an 317: 308: 233: 208: 1: 301: 7: 268: 10: 392: 314:Reiner (2003) pp. 44, 108 341:Oxford University Press 259: 277:, for the case where 260: 202: 156:-pure sublattice if 323:Reiner (2003) p. 45 255: 172:-pure sublattices 108:finitely generated 74:field of fractions 20:, in the field of 60:Formal definition 52:is embedded in a 383: 362: 324: 321: 315: 312: 295:Euclidean metric 264: 262: 261: 256: 136:Pure sublattices 131: 391: 390: 386: 385: 384: 382: 381: 380: 366: 365: 351: 328: 327: 322: 318: 313: 309: 304: 275:Lattice (group) 271: 203: 200: 199: 138: 119: 70:integral domain 62: 12: 11: 5: 389: 379: 378: 364: 363: 349: 337:Maximal Orders 326: 325: 316: 306: 305: 303: 300: 299: 298: 270: 267: 266: 265: 253: 250: 247: 244: 241: 238: 235: 232: 228: 225: 222: 219: 216: 213: 210: 207: 137: 134: 94:-vector space 61: 58: 56:vector space. 9: 6: 4: 3: 2: 388: 377: 376:Module theory 374: 373: 371: 360: 356: 352: 350:0-19-852673-3 346: 342: 338: 334: 330: 329: 320: 311: 307: 296: 292: 288: 284: 280: 276: 273: 272: 251: 248: 245: 242: 239: 236: 230: 226: 223: 220: 217: 214: 211: 205: 198: 197: 196: 194: 190: 187: 183: 179: 175: 171: 167: 163: 159: 155: 151: 147: 143: 133: 130: 126: 122: 117: 113: 109: 105: 101: 97: 93: 89: 86: 82: 78: 75: 71: 67: 57: 55: 51: 50:lattice group 47: 43: 39: 35: 31: 27: 23: 19: 336: 319: 310: 290: 286: 282: 278: 192: 188: 181: 177: 173: 169: 165: 161: 157: 153: 149: 145: 141: 139: 128: 124: 120: 115: 111: 103: 99: 95: 91: 87: 80: 76: 65: 63: 42:vector space 25: 15: 195:, given by 144:-submodule 22:ring theory 18:mathematics 359:1024.16008 333:Reiner, I. 302:References 293:, and the 246:∩ 234:↦ 221:⋅ 209:↦ 186:subspaces 114:. It is 85:submodule 370:Category 335:(2003). 269:See also 38:embedded 36:that is 100:lattice 44:over a 32:over a 26:lattice 357:  347:  79:. An 68:be an 30:module 281:is a 110:over 98:is a 90:of a 72:with 46:field 40:in a 28:is a 345:ISBN 180:and 116:full 64:Let 54:real 34:ring 24:, a 355:Zbl 191:of 176:of 164:is 148:of 140:An 118:if 106:is 102:if 16:In 372:: 353:. 343:. 132:. 127:ยท 123:= 361:. 291:R 287:V 283:Z 279:M 252:. 249:M 243:W 240:= 237:N 231:W 227:; 224:N 218:K 215:= 212:W 206:N 193:V 189:W 184:- 182:K 178:M 174:N 170:R 166:R 162:N 160:/ 158:M 154:R 150:M 146:N 142:R 129:M 125:K 121:V 112:R 104:M 96:V 92:K 88:M 83:- 81:R 77:K 66:R

Index

mathematics
ring theory
module
ring
embedded
vector space
field
lattice group
real
integral domain
field of fractions
submodule
finitely generated
subspaces
Lattice (group)
Euclidean metric
Reiner, I.
Oxford University Press
ISBN
0-19-852673-3
Zbl
1024.16008
Category
Module theory

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