User contributions for Hbghlyj
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5 May 2024
- 10:0310:03, 5 May 2024 diff hist +155 Decomposition of Field Extension as Separable Extension followed by Purely Inseparable Fixed {{explain|why?}} current
4 May 2024
- 15:1515:15, 4 May 2024 diff hist +95 Decomposition of Field Extension as Separable Extension followed by Purely Inseparable add one more step
- 15:1315:13, 4 May 2024 diff hist +259 m Definition:Separable Degree/Definition 2 Fixed {{NoSources}} current
- 15:1215:12, 4 May 2024 diff hist −340 Definition:Separable Degree fixed {{Mistake|move these onto the appropriate page}}
- 01:3501:35, 4 May 2024 diff hist +30 Steinitz's Theorem add more words
- 01:3301:33, 4 May 2024 diff hist +2,020 Steinitz's Theorem Add proof
- 01:0001:00, 4 May 2024 diff hist +65 m Primitive Element Theorem add more words
- 00:5700:57, 4 May 2024 diff hist −33 m Primitive Element Theorem not necessary to write " : E \longrightarrow \overline{F}" so removed it
- 00:5500:55, 4 May 2024 diff hist +5 m Primitive Element Theorem \bar to \overline
- 00:5400:54, 4 May 2024 diff hist 0 m Primitive Element Theorem Fix mistake
- 00:5300:53, 4 May 2024 diff hist +1,804 Primitive Element Theorem Add proof
- 00:2900:29, 4 May 2024 diff hist +1,122 Vector Space over an Infinite Field is not equal to the Union of Proper Subspaces Add proof
- 00:2000:20, 4 May 2024 diff hist +462 N Vector Space over an Infinite Field is not equal to the Union of Proper Subspaces add a theorem needed in the proof of primitive element theorem
3 May 2024
- 23:5723:57, 3 May 2024 diff hist +37 m Definition:Normal Extension sorry but I don't know what's wrong
- 23:5523:55, 3 May 2024 diff hist +71 Definition:Purely Inseparable Field Extension add MathWorld source current
- 23:4123:41, 3 May 2024 diff hist +101 m Separable Degree of Field Extensions is Multiplicative add more words
- 23:3823:38, 3 May 2024 diff hist +879 Separable Degree of Field Extensions is Multiplicative Add proof
- 23:2523:25, 3 May 2024 diff hist +511 N Talk:Separable Degree of Field Extensions is Multiplicative Created page with "== About different definitions == I read from [https://math.stackexchange.com/questions/591077/multiplicative-nature-of-the-separability-degree stackexchange]: If one starts with separability degree definition 2, as done in the book by Lang, the result follows without much difficulty. But it is intractable if one starts from definition 1 --~~~~" current
- 23:1223:12, 3 May 2024 diff hist +157 Steinitz's Theorem add a BookReference Tag: Visual edit: Switched
- 23:1123:11, 3 May 2024 diff hist +155 Primitive Element Theorem add a BookReference
- 23:0523:05, 3 May 2024 diff hist 0 m Equivalence of Definitions of Separable Degree To prove two numbers are equal, we only need prove one direction, so "2 implies 1" is not needed current
- 23:0223:02, 3 May 2024 diff hist −23 Equivalence of Definitions of Separable Degree Corrected the proof
- 22:5622:56, 3 May 2024 diff hist +3,344 N Equivalence of Definitions of Separable Degree Add proof
- 21:2521:25, 3 May 2024 diff hist +140 Separable Elements Form Field add a BookReference
- 21:2321:23, 3 May 2024 diff hist +140 Transitivity of Separable Field Extensions add a BookReference
- 20:2720:27, 3 May 2024 diff hist −61 m Steinitz's Theorem No edit summary
- 20:2620:26, 3 May 2024 diff hist +1,058 N Steinitz's Theorem A theorem needed in the proof of Primitive Element Theorem. name based on Wikipedia page https://en.wikipedia.org/wiki/Steinitz%27s_theorem_(field_theory)
- 20:2420:24, 3 May 2024 diff hist +41 Primitive Element Theorem Add "Also see"
- 20:2320:23, 3 May 2024 diff hist +15 m Primitive Element Theorem No edit summary
- 20:1120:11, 3 May 2024 diff hist +146 Primitive Element Theorem add a BookReference
- 20:0520:05, 3 May 2024 diff hist +171 Definition:Inseparable Degree add a BookReference
- 20:0120:01, 3 May 2024 diff hist −66 Definition:Embedding (Galois Theory) Undo revision 693226 by Hbghlyj (talk) current Tag: Undo
- 19:5519:55, 3 May 2024 diff hist −47 Separable Degree is At Most Equal To Degree Change $k$ to $F$
- 19:5319:53, 3 May 2024 diff hist +493 N Separable Degree of Field Extensions is Multiplicative Creating the page based on a theorem in Lang's book, which in needed in Transitivity of Separable Field Extensions
- 19:5219:52, 3 May 2024 diff hist −11 m Separable Degree is At Most Equal To Degree Typo
- 19:5219:52, 3 May 2024 diff hist +142 Separable Degree is At Most Equal To Degree Links
- 19:5119:51, 3 May 2024 diff hist +4 m Separable Degree is At Most Equal To Degree Typo
- 19:5119:51, 3 May 2024 diff hist +569 N Separable Degree is At Most Equal To Degree Creating the page based on a theorem in Lang's book, which in needed in Transitivity of Separable Field Extensions
- 19:4119:41, 3 May 2024 diff hist +167 Definition:Separable Degree Add a source
- 19:3719:37, 3 May 2024 diff hist +348 N Definition:Separable Degree/Definition 3 Created page with "== Definition == <onlyinclude> Let $K$ be a normal extension of $F$ that contains $E$. The '''separable degree''' $\index E F_{\operatorname {sep} }$ of $E / F$ is the number of embeddings of $E$ into $K$ that fix $F$. </onlyinclude> Category:Separable Field Extensions"
- 19:3619:36, 3 May 2024 diff hist +1 m Definition:Separable Degree/Definition 2 Add a blank line
- 19:3519:35, 3 May 2024 diff hist +344 N Definition:Separable Degree/Definition 2 Created page with "== Definition == <onlyinclude> Let $\bar F$ be the algebraic closure of $F$. The '''separable degree''' $\index E F_{\operatorname {sep} }$ of $E / F$ is the number of embeddings of $E$ into $\bar F$ that fix $F$. </onlyinclude> Category:Separable Field Extensions"
- 19:3219:32, 3 May 2024 diff hist +332 N Definition:Separable Degree/Definition 1 Created page with "== Definition == <onlyinclude> Let $S \subseteq E$ be the separable closure of $F$ in $E$. The '''separable degree''' $\index E F_{\operatorname {sep} }$ of $E / F$ is the degree $\index S F$. </onlyinclude> Category:Separable Field Extensions"
- 19:3119:31, 3 May 2024 diff hist 0 m Definition:Separable Degree Move multiple definitions to separate pages
- 19:3019:30, 3 May 2024 diff hist +91 Definition:Separable Degree Move multiple definitions to separate pages
- 19:2719:27, 3 May 2024 diff hist +139 Definition:Inseparable Degree Fixed {{NoSources}}
- 19:2619:26, 3 May 2024 diff hist −15 m Definition:Separable Degree Add a period
- 19:2519:25, 3 May 2024 diff hist +155 m Definition:Separable Degree Fixed {{NoSources}}
- 19:1919:19, 3 May 2024 diff hist +499 Decomposition of Field Extension as Separable Extension followed by Purely Inseparable Fixed {{proof wanted|use transitivity of separable extensions}}
- 19:1019:10, 3 May 2024 diff hist +331 Separable Elements Form Field Fixed {{NoSources}}