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    Let  F \subset L be a field extension and  A \subset L be a subset we define the intermediate field as the subfield of  L where we "add" the elements of  A and denote this subfield as  K(A).

    How does one figure out how the elements of such a field look like?

    Example:

    Suppose we take the extension  \mathbb{Q} \subset \Bbb{C} then we let the subset of  \mathbb{C} be  \{i,e,\pi \} for example what how can we describe the elements of  \mathbb{Q}(i,e, \pi).

    What I mean by that is  \mathbb{R}(i)=\{a+bi : a,b \in \mathbb{R}\}=\Bbb{C} or  \mathbb{Q}(i)=\{a+bi : a,b \in \mathbb{Q}\}.

    I believe these are called the Gaussian integers

    .But when the subset has a few elements more it's confusing me as to what they elements look like.

    Hopefully what I've posted makes some sense at least my algebra is quite poor.
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    Must be some bug, happening to me as well.
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    Happened to me last night as well.
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    (Original post by cliveb2016)
    I need to ask a question but the latex is not compiling any ideas why?
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    Let  F \subset L be a field extension and  A \subset L be a subset we define the intermediate field as the subfield of  L where we "add" the elements of  A and denote this subfield as  K(A).How does one figure out how the elements of such a field look like?Example suppose we take the extension  \mathbb{Q} \subset \Bbb{C} then we let the subset of  \mathbb{R} be  \{i,e,\pi \} for example what how can we describe the elements of  \mathbb{Q}(i,e, \pi).What I mean by that is  \mathbb{R}(i)=\{a+bi : a,b \in \mathbb{R}\}=\Bbb{C} or  \mathbb{Q}(i)=\{a+bi : a,b \in \mathbb{Q}\}, I believe these are called the Gaussian integers.But when the subset has a few elements more it's confusing me as to what they elements look like.Hopefully what I've posted makes some sense at least my algebra is quite poor.
    Seems to be working again.
 
 
 
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