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are
Noetherian. This is in contrast to the general situation with finitely generated modules: a submodule of a finitely generated module need not be finitely generated.
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the left-right adjectives may be dropped as they are unnecessary. Also, if
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who was the first one to discover the true importance of the property.
381:"commutative algebra - Is every Noetherian module finitely generated?"
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structures as well: a
Noetherian bimodule is a bimodule whose
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was the first mathematician to work with the properties of
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Commutative
Algebra with a View Toward Algebraic Geometry
236:Any finitely generated right module over a right
233:Any module that is finite as a set is Noetherian.
283:The Noetherian condition can also be defined on
95:, two other characterizations are possible:
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122:All of the submodules of the module are
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256:is, by definition, a Noetherian right
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334:Ascending/descending chain condition
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174:of integers, is a Noetherian module.
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107:of submodules of the module has a
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218:can be made into a module using
87:Characterizations and properties
315:-module were Noetherian, then
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59:an important theorem known as
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445:Graduate Texts in Mathematics
53:finitely generated submodules
447:(Third ed.), Springer,
226:on the left of elements of
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385:Mathematics Stack Exchange
344:Finitely generated module
30:ascending chain condition
430:, Springer-Verlag, 1995.
303:is in particular a left
115:). This is known as the
441:Advanced Linear Algebra
406:, p. 133 §5 Theorem 5.7
245:Use in other structures
240:is a Noetherian module.
91:In the presence of the
61:Hilbert's basis theorem
311:considered as a left
220:matrix multiplication
67:in the multivariate
63:which says that any
476:Commutative algebra
28:that satisfies the
339:Composition series
195:over a field, and
138:a submodule, then
124:finitely generated
77:finitely generated
454:978-0-387-72828-5
117:maximum condition
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193:matrix ring
465:Categories
416:Roman 2008
404:Roman 2008
390:2022-05-04
368:Roman 2008
355:References
34:submodules
426:Eisenbud
299:bimodule
42:inclusion
439:(2008),
323:See also
285:bimodule
249:A right
168:integers
161:Examples
101:nonempty
214:, then
49:Hilbert
32:on its
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57:proved
26:module
289:poset
272:is a
73:field
65:ideal
55:. He
24:is a
449:ISBN
172:ring
166:The
149:and
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99:Any
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177:If
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