# What is Extension: Definition and 293 Discussions

A filename extension, file extension or file type is an identifier specified as a suffix to the name of a computer file. The extension indicates a characteristic of the file contents or its intended use. A filename extension is typically delimited from the filename with a full stop (period), but in some systems it is separated with spaces.
Some file systems implement filename extensions as a feature of the file system itself and may limit the length and format of the extension, while others treat filename extensions as part of the filename without special distinction.

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43. ### Having trouble deciding my masters (and by extension, my future)

Hey there, i guess i just need to ventilate some and see what people think about my situation and about the choices i have. First of all i must say that i am from Sweden and therefore i have conditions that few other people have. I get my education for free and i am free to chose whatever field...
44. ### Question: Why is this Extension Normal?

Homework Statement I'm following the solutions to a homework tutorial and I'm having trouble understanding why what they're saying is true. Question: Let f be a polynomial in K[x] and let S be the splitting field of f over K. decide whether the extension S:K is galois and describe the...
45. ### Some true or false Field extension theory questions

Homework Statement Let S= {e^2*i*pi/n for all n in the natural numbers} and let F=Q Is F:Q 1) algebraic? 2) finite? 3) simple? 4)separable? Homework EquationsThe Attempt at a Solution 1) Every element in S is a root of x^n-1 and every element of a in Q is a root of x-a, and thus I think...
46. ### Calculating Galois Group of extension

Homework Statement Let c be a primitive 3rd root of unity and b be the third real root of four. Now consider the extension Q(c,b):Q. Find the degree of this extension, show that it is Galois, and calculate Gal(Q(c,b):Q) and then use the Galois group to calculate all intermediate fields...
47. ### Determining Galois extension based on degree of extension

Homework Statement If Char(K) = 0 and [L:K]=2, is L:K a galois extension? Homework EquationsThe Attempt at a Solution My gut is saying yes because if [L:K]=2 then it seems that any polynomial in K[x] with a root in L should split in L[x]. Something about how some hypothetical minimal...
48. ### Galois Extension with intermediate field that is not Galois

Homework Statement Hey PF, I'm trying to find fields K<M<L such that K:L is Galois but K:M is not. Homework EquationsThe Attempt at a Solution My first idea was let K=Q the field of rational numbers and c be a primitive 6th root of unity, so then Q<Q(c^4)<Q(c). Q:Q(c) Is galois, and I'm...
49. ### Is this a Galois extension?

Homework Statement Let Q < L < Q(c) where c is a primitive nth root of unity over Q. Is [L:Q] a Galois extension? Homework EquationsThe Attempt at a Solution L must be equal to Q(d) where d is a non primitive nth root of unity. [Q(d):Q] is not a galois extension because the minimal polynomial...
50. ### Is this field extension normal?

Homework Statement Consider the field extension Q(c):Q, where c is a primitive nth root of unity. Is this extension normal? Homework EquationsThe Attempt at a Solution I believe this polynomial splits in x^n - 1,where it's n roots are exactly the powers of c. Thus this extension is normal...