81:
71:
53:
22:
248:
This section is incredibly confusing. Every paragraph flips back and forth between the two definitions of primitive element and generator, (#1) where successive powers of which yield a field's multiplicative group, and (#2) the element that creates the field extension L.
155:
The discussion of the other definition of "primitive element" (for finite fields) is weak. The two usages are somewhat different, it is true, but there does not need to be so many words spent on it. Or something.
133:
179:
good place to put a careful discussion of the difference between a simple algebraic and a simple transcendental extension. I think there might be something roughly like that in
309:
255:
How does the general definition require that? Also, "polynomial in the generator" is confusing, it should read more like "a polynomial who's indeterminate is θ.
127:
304:
103:
157:
265:
94:
58:
206:
I tried to expand and clarify the article on the points you have mentioned, but I am not completely satisfied with the result.
252:"Thus the general definition requires that every element of the field may be expressed as a polynomial in the generator,"
33:
226:
161:
21:
269:
234:
39:
80:
261:
102:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
285:
230:
86:
70:
52:
222:
207:
198:
184:
180:
258:
Finally it's not clear what the equation L=K(θ) means. K is a field, not a function.
298:
281:
188:
229:
have much in common and neither is particularly long -- could they be unified?
99:
76:
289:
273:
238:
210:
201:
191:
165:
15:
183:, but it would be much cleaner to put it here. The article
187:
is probably a bit too long, too many facts squeezed in.
98:, a collaborative effort to improve the coverage of
132:This article has not yet received a rating on the
8:
19:
259:
47:
49:
310:Unknown-priority mathematics articles
7:
92:This article is within the scope of
38:It is of interest to the following
280:I agree, and I have rewritten it.
14:
112:Knowledge:WikiProject Mathematics
305:Start-Class mathematics articles
115:Template:WikiProject Mathematics
79:
69:
51:
20:
1:
239:06:55, 1 September 2008 (UTC)
166:23:39, 27 December 2012 (UTC)
106:and see a list of open tasks.
326:
290:11:26, 15 March 2022 (UTC)
274:08:13, 15 March 2022 (UTC)
211:14:54, 23 April 2006 (UTC)
202:11:30, 23 April 2006 (UTC)
197:I will see what I can do.
192:18:29, 18 April 2006 (UTC)
227:primitive element theorem
131:
64:
46:
175:This article would be a
134:project's priority scale
95:WikiProject Mathematics
28:This article is rated
118:mathematics articles
171:Careful Discussion
87:Mathematics portal
34:content assessment
276:
264:comment added by
148:
147:
144:
143:
140:
139:
317:
223:Simple extension
120:
119:
116:
113:
110:
89:
84:
83:
73:
66:
65:
55:
48:
31:
25:
24:
16:
325:
324:
320:
319:
318:
316:
315:
314:
295:
294:
246:
219:
185:field extension
181:field extension
173:
153:
117:
114:
111:
108:
107:
85:
78:
32:on Knowledge's
29:
12:
11:
5:
323:
321:
313:
312:
307:
297:
296:
293:
292:
245:
242:
218:
215:
214:
213:
204:
172:
169:
158:84.226.161.197
152:
149:
146:
145:
142:
141:
138:
137:
130:
124:
123:
121:
104:the discussion
91:
90:
74:
62:
61:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
322:
311:
308:
306:
303:
302:
300:
291:
287:
283:
279:
278:
277:
275:
271:
267:
263:
256:
253:
250:
243:
241:
240:
236:
232:
231:Richard Pinch
228:
224:
221:The articles
216:
212:
209:
205:
203:
200:
196:
195:
194:
193:
190:
186:
182:
178:
170:
168:
167:
163:
159:
150:
135:
129:
126:
125:
122:
105:
101:
97:
96:
88:
82:
77:
75:
72:
68:
67:
63:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
266:108.60.43.48
260:— Preceding
257:
254:
251:
247:
220:
176:
174:
154:
93:
40:WikiProjects
217:Unification
109:Mathematics
100:mathematics
59:Mathematics
30:Start-class
299:Categories
244:Definition
208:MathMartin
199:MathMartin
282:D.Lazard
262:unsigned
189:Dmharvey
177:really
36:scale.
286:talk
270:talk
235:talk
225:and
162:talk
151:Weak
128:???
301::
288:)
272:)
237:)
164:)
284:(
268:(
233:(
160:(
136:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
