Jeff
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 Nov29 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 $\sigma_k$. Nov28 answered Abstract Algebra: Field extensions Nov25 comment Important topics to cover in an intro course to algebraic number theory? I can't upvote this answer enough. Oct9 answered Differences between infinite-dimensional and finite-dimensional vector spaces Oct3 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. Oct3 comment Properties of Linear Transformations? Oh, and $\mathbf{R}^n$ is an example of a vector space. Oct3 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. Oct3 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 Oct2 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/… Oct2 answered Why can Echelon Matrices have zero rows but Echelon systems can't have any equations with no leading variables? Sep29 answered Visualising finite fields Sep14 suggested rejected edit on Demonstração do Teorema de Bezout. (Proof of Bézout's Theorem) Sep13 answered Ramification index in number fields extension Aug23 awarded Necromancer Aug14 answered How the ring of algebraic numbers looks like? Jul28 answered How can a function's range be 'the reals including infinity' Jun28 comment Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces? $\mathbb{C} \otimes _\mathbb{C} \mathbb{C} \simeq \mathbb{C}$ Jun16 comment A subset of a field that is a subfield This is definitely what the problem-writer had in mind. Jun11 comment '$R$-rational points,' where $R$ is an arbitrary ring Yes, but that edit button is so far away... Jun11 comment '$R$-rational points,' where $R$ is an arbitrary ring We seem to have posted at the same time, but I like your answer better =D