155:
31:
on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite length. Noetherian objects are named after
81:
is said to be
Noetherian if there is no infinitely increasing filtration of it by subobjects. A category is Noetherian if every object in it is Noetherian.
187:
163:
192:
94:
111:, also called well-founded induction, a proof method for binary relations that satisfy the descending chain condition.
115:
28:
78:
125:
108:
71:
173:
incorrectly led you here, you may wish to change the link to point directly to the intended article.
35:, who was the first to study the ascending and descending chain conditions for rings. Specifically:
84:
43:
133:
129:
57:
121:
98:
67:
39:
88:
61:
53:
24:
181:
146:
32:
166:
includes a list of related items that share the same name (or similar names).
102:
17:
154:
47:
149:, a ring that satisfies the descending chain condition on ideals.
91:
that satisfies the ascending chain condition on its elements.
74:
that satisfies the ascending chain condition on submodules.
170:
101:that satisfies the descending chain condition on
60:that satisfies the ascending chain condition on
46:that satisfies the ascending chain condition on
160:Index of articles associated with the same name
8:
29:ascending or descending chain condition
132:that admits a finite covering by open
7:
14:
188:Set index articles on mathematics
153:
114:Noetherian rewriting system, an
77:More generally, an object in a
1:
118:that has no infinite chains.
95:Noetherian topological space
209:
152:
116:abstract rewriting system
193:Mathematical analysis
136:of Noetherian rings.
109:Noetherian induction
23:is used to describe
16:In mathematics, the
85:Noetherian relation
130:algebraic geometry
164:set index article
122:Noetherian scheme
99:topological space
68:Noetherian module
200:
174:
157:
40:Noetherian group
27:that satisfy an
208:
207:
203:
202:
201:
199:
198:
197:
178:
177:
176:
175:
168:
167:
161:
143:
89:binary relation
54:Noetherian ring
12:
11:
5:
206:
204:
196:
195:
190:
180:
179:
159:
158:
151:
150:
142:
139:
138:
137:
119:
112:
106:
92:
82:
75:
65:
51:
13:
10:
9:
6:
4:
3:
2:
205:
194:
191:
189:
186:
185:
183:
172:
171:internal link
165:
156:
148:
147:Artinian ring
145:
144:
140:
135:
131:
127:
123:
120:
117:
113:
110:
107:
104:
100:
96:
93:
90:
86:
83:
80:
76:
73:
69:
66:
63:
59:
55:
52:
49:
45:
41:
38:
37:
36:
34:
30:
26:
22:
19:
33:Emmy Noether
20:
15:
103:closed sets
182:Categories
21:Noetherian
48:subgroups
18:adjective
141:See also
79:category
134:spectra
25:objects
169:If an
126:scheme
72:module
62:ideals
162:This
44:group
124:, a
97:, a
87:, a
70:, a
58:ring
56:, a
42:, a
128:in
184::
105:.
64:.
50:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.