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Dec
12
answered What is the basis of basis?
Nov
29
comment Abstract Algebra: Field extensions
Right. The norm will be fixed since the composition of two automorphisms $\sigma_i$ and $\sigma_j$ is another automorphism $\sigma_k$.
Nov
28
answered Abstract Algebra: Field extensions
Nov
25
comment Important topics to cover in an intro course to algebraic number theory?
I can't upvote this answer enough.
Oct
9
answered Differences between infinite-dimensional and finite-dimensional vector spaces
Oct
3
comment Properties of Linear Transformations?
Very often, the motivation for studying a map $T:A \to B$ between algebraic objects is a scenario where we understand $B$ very well, and we wish to understand $A$ better. In order to be able to transfer information from $B$ back to $A$, we need our map $T$ to preserve the relevant structures.
Oct
3
comment Properties of Linear Transformations?
Oh, and $\mathbf{R}^n$ is an example of a vector space.
Oct
3
comment Properties of Linear Transformations?
they are somehow less useful to study. If you study more mathematics, you will encounter many more examples of this sort of thing, and it will make more sense then.
Oct
3
comment Properties of Linear Transformations?
Jared's answer is focusing on the intuition. Mathematicians study many different types of objects; a vector space is an example of what might be called an algebraic object. A vector space is composed of things called vectors, and there are two operations you can carry out with these vectors: you can add them together, or you can scale them. So if we want to study maps (that is, functions) between two vector spaces, the best ones to consider will be the maps which respect those two operations. Thus, we get the definition of a linear transformation. Other maps between vector spaces exist, but
Oct
2
comment Why learning modern algebraic geometry is so complicated?
I feel compelled to link to this post on MO regarding the usefulness of studying EGA: mathoverflow.net/questions/3041/…
Oct
2
answered Why can Echelon Matrices have zero rows but Echelon systems can't have any equations with no leading variables?
Sep
29
answered Visualising finite fields
Sep
14
suggested rejected edit on Demonstração do Teorema de Bezout. (Proof of Bézout's Theorem)
Sep
13
answered Ramification index in number fields extension
Aug
23
awarded  Necromancer
Aug
14
answered How the ring of algebraic numbers looks like?
Jul
28
answered How can a function's range be 'the reals including infinity'
Jun
28
comment Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?
$\mathbb{C} \otimes _\mathbb{C} \mathbb{C} \simeq \mathbb{C}$
Jun
16
comment A subset of a field that is a subfield
This is definitely what the problem-writer had in mind.
Jun
11
comment '$R$-rational points,' where $R$ is an arbitrary ring
Yes, but that edit button is so far away...