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205: 262: 246: 303: 239: 332: 296: 232: 190: 337: 322: 289: 327: 204: 17: 212: 167: 162: 73: 24: 186: 65: 39: 157: 129: 42: 273: 269: 216: 179: 148:. This includes the cases of local rings and finite dimensional algebras over fields. 109: 316: 121: 261: 184:
Commutative algebra with a view toward Algebraic Geometry
277: 220: 88:). In the case of local rings with maximal ideal 297: 240: 8: 144:) is a semisimple module and is the top of 304: 290: 247: 233: 64:) denotes the intersection of all proper 7: 258: 256: 201: 199: 112:(=semi-artinian ring), that is, if 14: 260: 203: 1: 276:. You can help Knowledge by 219:. You can help Knowledge by 354: 255: 198: 333:Commutative algebra stubs 52:For finite-dimensional 272:-related article is a 215:-related article is a 74:radical of the module 338:Linear algebra stubs 16:In the context of a 323:Commutative algebra 213:commutative algebra 168:Socle (mathematics) 163:Radical of a module 76:), then the top of 60:a field) R, if rad( 66:maximal submodules 285: 284: 228: 227: 104:. In general if 345: 306: 299: 292: 264: 257: 249: 242: 235: 207: 200: 158:Projective cover 130:Jacobson radical 353: 352: 348: 347: 346: 344: 343: 342: 313: 312: 311: 310: 254: 253: 196: 176: 154: 49:if it exists. 43:quotient module 38:is the largest 12: 11: 5: 351: 349: 341: 340: 335: 330: 325: 315: 314: 309: 308: 301: 294: 286: 283: 282: 270:linear algebra 265: 252: 251: 244: 237: 229: 226: 225: 208: 194: 193: 180:David Eisenbud 175: 172: 171: 170: 165: 160: 153: 150: 110:semilocal ring 13: 10: 9: 6: 4: 3: 2: 350: 339: 336: 334: 331: 329: 328:Module theory 326: 324: 321: 320: 318: 307: 302: 300: 295: 293: 288: 287: 281: 279: 275: 271: 266: 263: 259: 250: 245: 243: 238: 236: 231: 230: 224: 222: 218: 214: 209: 206: 202: 197: 192: 191:0-387-94269-6 188: 185: 181: 178: 177: 173: 169: 166: 164: 161: 159: 156: 155: 151: 149: 147: 143: 139: 135: 131: 127: 123: 122:Artinian ring 119: 115: 111: 107: 103: 99: 95: 92:, the top of 91: 87: 83: 79: 75: 71: 67: 63: 59: 55: 50: 48: 44: 41: 37: 33: 29: 26: 22: 19: 278:expanding it 267: 221:expanding it 210: 195: 183: 145: 141: 137: 133: 125: 124:, where Rad( 117: 113: 105: 101: 97: 93: 89: 85: 81: 77: 69: 61: 57: 53: 51: 46: 35: 31: 27: 20: 15: 56:-algebras ( 317:Categories 174:References 40:semisimple 128:) is the 152:See also 120:) is an 136:, then 23:over a 189:  30:, the 18:module 268:This 211:This 140:/rad( 116:/Rad( 108:is a 84:/rad( 72:(the 274:stub 217:stub 187:ISBN 25:ring 132:of 96:is 80:is 68:of 45:of 34:of 32:top 319:: 182:, 102:PM 305:e 298:t 291:v 280:. 248:e 241:t 234:v 223:. 146:M 142:M 138:M 134:R 126:R 118:R 114:R 106:R 100:/ 98:M 94:M 90:P 86:M 82:M 78:M 70:M 62:M 58:k 54:k 47:M 36:M 28:R 21:M

Index

module
ring
semisimple
quotient module
maximal submodules
radical of the module
semilocal ring
Artinian ring
Jacobson radical
Projective cover
Radical of a module
Socle (mathematics)
David Eisenbud
ISBN
0-387-94269-6
Stub icon
commutative algebra
stub
expanding it
v
t
e
Stub icon
linear algebra
stub
expanding it
v
t
e
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