Talk:Simple extension

Weak

The discussion of the other definition of "primitive element" (for finite fields) is weak. The two usages are somewhat different, it is true, but there does not need to be so many words spent on it. Or something. 84.226.161.197 (talk) 23:39, 27 December 2012 (UTC)[reply]

Careful Discussion

This article would be a really good place to put a careful discussion of the difference between a simple algebraic and a simple transcendental extension. I think there might be something roughly like that in field extension, but it would be much cleaner to put it here. The article field extension is probably a bit too long, too many facts squeezed in. Dmharvey 18:29, 18 April 2006 (UTC)[reply]

I will see what I can do. MathMartin 11:30, 23 April 2006 (UTC)[reply]

I tried to expand and clarify the article on the points you have mentioned, but I am not completely satisfied with the result. MathMartin 14:54, 23 April 2006 (UTC)[reply]

Unification

The articles Simple extension and primitive element theorem have much in common and neither is particularly long -- could they be unified? Richard Pinch (talk) 06:55, 1 September 2008 (UTC)[reply]

Definition

This section is incredibly confusing. Every paragraph flips back and forth between the two definitions of primitive element and generator, (#1) where successive powers of which yield a field's multiplicative group, and (#2) the element that creates the field extension L.

"Thus the general definition requires that every element of the field may be expressed as a polynomial in the generator,"

How does the general definition require that? Also, "polynomial in the generator" is confusing, it should read more like "a polynomial who's indeterminate is θ.

Finally it's not clear what the equation L=K(θ) means. K is a field, not a function. — Preceding unsigned comment added by 108.60.43.48 (talk) 08:13, 15 March 2022 (UTC)[reply]

I agree, and I have rewritten it. D.Lazard (talk) 11:26, 15 March 2022 (UTC)[reply]