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4:23 AM
A new tag: .
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Q: A statement about normal basis element , trace and characteristic of field

Saun DevLet $F/K$ be a normal finite extension where $F=F_1 \times F_2$ for subfields $F_1,F_2$ of $F$ where $F_1\ne F$ . Suppose $w$ is a normal basis element in $F/K$ for any $w\in F$ for which $Tr_{F/F_2}(w)$ is a normal basis element in $F_2/K$ . Then is it true that $K$ has prime characteristic ?

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Q: Another statement about normal basis element , trace and characteristic of field

Saun DevLet $F/K$ be a normal finite extension where $F=F_1 \times F_2$ for subfields $F_1,F_2$ of $F$ where $F_1\ne F$ . Suppose $K$ has prime characteristic . Then is it true that $w$ is a normal basis element in $F/K$ for any $w\in F$ for which $Tr_{F/F_2}(w)$ is a normal basis element in $F_2/K$ ? ...

 
 
8 hours later…
12:38 PM
A new tag: - created by Leila Hatami.
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Q: Invariance of Eigenvalues of a matrix

LeilaSuppose that $G$ is a signed graph (a graph in which each edge has a positive of negative sign) Define Adjacency matrix of $G$ as before except that we have $+1$ for positive edges and $-1$ Prove that the eigen values of Adjacency matrix will not change if you multiply some rows and columns by...

In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. Three fundamental questions about a signed graph are: Is it balanced? What is the largest size of a balanced edge set in it? What is the smallest number of vertices that must be deleted to make it balanced? The first question is easy to solve quickly; the second and third are computationally intractable (technically, they are NP-hard). Signed graphs appeared first in a mathematical paper...
@Leila I see that you have created (signed-graph) tag. It might be useful to create also tag-wiki or at least tag-excerpt. It might help other users to use the tag correctly. (This is probably not a problem here, since the tag name seems to be descriptive enough.) Another reason is that the tags used on only one question are automatically deleted after certain time unless they have tag-wiki. — Martin Sleziak 6 mins ago
 
1:29 PM
@MartinSleziak Thanks. Done! — Leila 5 mins ago
The suggested edits for the tag-wiki and tag-excerpt are currently pending.
And now there is tag-excerpt and tag-wiki.
 
 
1 hour later…
2:48 PM
Only now I notice that there used to be tag. On a more serious note, I have added tag to this question: Why do you answer questions on math.stackexchange? If it is not a good fit, feel free to remove it.
@quid I am not sure whether you remember our discussion about and tags related to maximization. Some of them have been synonyms for a long time, the tag is a suggested synonym which is currently at +2.
I just wanted to remind you this issue. (You mentioned a possibility that you make a post on meta about this.)
 

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