177:
218:
211:
247:
204:
151:
237:
43:
176:
242:
184:
21:
107:
50:
147:
111:
79:
58:
29:
161:
157:
83:
62:
188:
231:
74:
Connectedness defines a fairly general class of commutative rings. For example, all
87:
17:
75:
146:(2 ed.), New York: W. H. Freeman and Company, pp. xviii+686,
98:; here the element (1, 0) is a non-trivial idempotent.
35:
that satisfies one of the following equivalent conditions:
42:
possesses no non-trivial (that is, not equal to 1 or 0)
192:
110:, connectedness is generalized to the concept of a
212:
8:
219:
205:
86:are connected. Non-examples are given by
130:
123:
7:
173:
171:
82:are connected. In particular, all
14:
175:
1:
20:, especially in the field of
191:. You can help Knowledge by
264:
170:
248:Commutative algebra stubs
142:Jacobson, Nathan (1989),
70:Examples and non-examples
187:-related article is a
238:Commutative algebra
185:commutative algebra
44:idempotent elements
22:commutative algebra
108:algebraic geometry
200:
199:
144:Basic algebra. II
80:irreducible rings
255:
221:
214:
207:
179:
172:
164:
134:
128:
112:connected scheme
84:integral domains
59:Zariski topology
30:commutative ring
263:
262:
258:
257:
256:
254:
253:
252:
228:
227:
226:
225:
168:
154:
141:
138:
137:
129:
125:
120:
104:
102:Generalizations
78:and all (meet-)
72:
63:connected space
12:
11:
5:
261:
259:
251:
250:
245:
240:
230:
229:
224:
223:
216:
209:
201:
198:
197:
180:
166:
165:
152:
136:
135:
122:
121:
119:
116:
103:
100:
71:
68:
67:
66:
47:
26:connected ring
13:
10:
9:
6:
4:
3:
2:
260:
249:
246:
244:
241:
239:
236:
235:
233:
222:
217:
215:
210:
208:
203:
202:
196:
194:
190:
186:
181:
178:
174:
169:
163:
159:
155:
153:0-7167-1933-9
149:
145:
140:
139:
132:
131:Jacobson 1989
127:
124:
117:
115:
113:
109:
101:
99:
97:
94: ×
93:
89:
88:product rings
85:
81:
77:
69:
64:
60:
56:
52:
48:
45:
41:
38:
37:
36:
34:
31:
27:
23:
19:
193:expanding it
182:
167:
143:
126:
105:
95:
91:
73:
54:
39:
32:
25:
15:
243:Ring theory
76:local rings
18:mathematics
232:Categories
118:References
57:with the
133:, p 418.
90:such as
51:spectrum
162:1009787
160:
150:
183:This
61:is a
28:is a
189:stub
148:ISBN
49:the
24:, a
106:In
53:of
16:In
234::
158:MR
156:,
114:.
220:e
213:t
206:v
195:.
96:Z
92:Z
65:.
55:A
46:;
40:A
33:A
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.