# Tagged Questions

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### What is Abstract Algebra essentially?

In the most basic sense, what is abstract algebra about? Wolfram Mathworld has the following definition: "Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic ...
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### Construction of the Hyperreal numbers

Several times I have seen questions/answers here about using the correct definition of derivatives. There are also questions about whether or not $1/0$ is defined. Sometimes there is a discussion ...
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### Mathematics and Origami

I am reading through this paper about the math behind origami: http://www.math.washington.edu/~morrow/336_09/papers/Sheri.pdf However, I am getting confused with definitions 3.3 and 3.4. I am not sure ...
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### Math and Origami

I am working on a project for class about the mathematics behind origami and write now I am looking into what is and is not constructible. I've gotten to the definition of origami constructible points ...
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### Is $\Bbb Q[\sqrt2]$ cyclotomic?

This overview of Galois Theory claims that a field extension of $F$ is cyclotomic if it's obtained by adjoining an $n$th root of any element of $F$. Wikipedia claims you have to adjoin a root of unity ...
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### Understanding of extension fields with Kronecker's thorem

In the book Contemporary Abstract Algebra by Gallian it defines an extension field as follows: A field $E$ is an extension field of a field $F$ if $F\subseteq E$ and the operations of $F$ are ...
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### What is the meaning of $K/F$ is a cyclic extension?

I have it that $K/F$ is a (finite) field extension, what is the definition of when $K/F$ is called cyclic ? I heard it while I studied Galois theory and it was defined as $K/F$ is called cyclic ...
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### Definition of Separability Degree

For an assignment, I am trying to determine the separability degree of some algebraic field extension $L/K$. The definition of the separability degree of polynomial is not difficult to find at all, ...
Could someone possibly explain this definition (applied to fields) to me? The principle of substitution: In a field F, we can, in any formula involving an element $\alpha\in F$, replace $\alpha$ ...