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149:{\displaystyle \operatorname {GKdim} =\sup _{V,M_{0}}\limsup _{n\to \infty }\log _{n}\dim _{k}M_{0}V^{n}}
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350:≥ 2, there exists a finitely generated algebra whose GK dimension is
505:
Coutinho: A primer of algebraic D-modules. Cambridge, 1995
417:
for the
Gelfand–Kirillov dimension and finally to prove
555:
244:
The
Gelfand–Kirillov dimension of a finitely generated
401:
over the Weyl algebra coincides with the dimension of
376:
287:
201:
175:
54:
389:
328:
220:
187:
148:
484:Proceedings of the American Mathematical Society
85:
62:
575:
437:, and these modules play a great role in the
235:if its Gelfand–Kirillov dimension is finite.
8:
405:, which is by definition the degree of the
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76:
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53:
476:"A remark on Gelfand–Kirillov dimension"
474:Smith, S. Paul; Zhang, James J. (1998).
450:
278:In particular, the GK dimension of the
413:. This enables to prove additivity in
457:
421:, which states that the dimension of
7:
536:
534:
433:as those with the minimal dimension
397:, the Gelfand–Kirillov dimension of
554:. You can help Knowledge (XXG) by
429:. This leads to the definition of
95:
14:
538:
323:
291:
221:{\displaystyle M_{0}\subset M}
92:
1:
498:10.1090/S0002-9939-98-04074-X
439:geometric Langlands program
231:An algebra is said to have
627:
533:
359:In the theory of D-Modules
188:{\displaystyle V\subset A}
22:Gelfand–Kirillov dimension
550:-related article is a
521:"Noncommutative Rings"
419:Bernstein's inequality
391:
330:
222:
189:
150:
415:short exact sequences
392:
390:{\displaystyle A_{n}}
363:Given a right module
331:
275:over the base field.)
263:(or equivalently the
223:
190:
151:
374:
285:
265:transcendence degree
199:
173:
52:
431:holonomic D-modules
343:(Warfield) For any
246:commutative algebra
407:Hilbert polynomial
387:
326:
269:field of fractions
218:
185:
165:finite-dimensional
163:is taken over all
146:
99:
83:
563:
562:
460:, Theorem VI.2.1.
425:must be at least
329:{\displaystyle k}
233:polynomial growth
84:
61:
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601:Abstract algebra
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510:Further reading
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280:polynomial ring
257:Krull dimension
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517:Artin, Michael
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491:(2): 349–352.
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86:lim sup
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71:
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13:
10:
9:
6:
4:
3:
2:
623:
612:
611:Algebra stubs
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526:. Chapter VI.
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28:) of a right
27:
23:
19:
556:expanding it
545:
530:
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422:
410:
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398:
369:Weyl algebra
364:
362:
351:
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260:
248:
232:
230:
158:
42:
37:
32:
26:GK dimension
25:
21:
15:
345:real number
239:Basic facts
595:Categories
468:References
458:Artin 1999
159:where the
606:Dimension
367:over the
308:…
213:⊂
180:⊂
168:subspaces
124:
111:
96:∞
93:→
519:(1999).
161:supremum
40:-algebra
548:algebra
267:of the
255:is the
251:over a
35:over a
18:algebra
30:module
20:, the
546:This
524:(PDF)
479:(PDF)
445:Notes
253:field
56:GKdim
552:stub
195:and
45:is:
24:(or
493:doi
489:126
409:of
336:Is
271:of
259:of
115:dim
102:log
63:sup
16:In
597::
487:.
481:.
441:.
228:.
583:e
576:t
569:v
558:.
501:.
495::
435:n
427:n
423:M
411:M
403:M
399:M
383:n
379:A
365:M
354:.
352:r
348:r
340:.
338:n
324:]
319:n
315:x
311:,
305:,
300:1
296:x
292:[
289:k
273:A
261:A
249:A
216:M
208:0
204:M
183:A
177:V
142:n
138:V
132:0
128:M
119:k
106:n
90:n
78:0
74:M
70:,
67:V
59:=
43:A
38:k
33:M
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