Textbooks
I recently added two new pages to the blog: a bibliography for listing references I cite on multiple occasions, and a suggestions and requests page. The bibliography is likely to soon contain citations...
View ArticleClik here to view.
Functoriality
I wanted to talk about the geometric interpretation of localization, but before I do so I should talk more generally about the relationship between ring homomorphisms on the one hand and continuous...
View ArticleClik here to view.
Affine varieties and regular maps
I have to admit I’ve been using somewhat unconventional definitions. The usual definition of an affine variety is as an irreducible Zariski-closed subset of , affine -space over an algebraically closed...
View ArticleClik here to view.
MaxSpec is not a functor
For commutative unital C*-algebras and for finitely-generated reduced integral -algebras, we have seen that is a functor which sends homomorphisms to continuous functions. However, this is not true for...
View ArticleClik here to view.
Localization and the strong Nullstellensatz
A basic idea in topology and analysis is to study a space by restricting attention to arbitrarily small neighborhoods of a point. It is desirable, therefore, to have a notion of looking at small...
View ArticleAdjectives
Apropos of nothing, I now have a new favorite mathematical term: “Fake baby monster Lie algebra.” And I thought “complex simple Lie algebra” was funny.
View ArticleClik here to view.
The connected components functor
I skimmed through books 1, 4, and 5 of my new batch and am currently skimming through 3; it seems I don’t have the mathematical prerequisites to get much out of 2. It will take me a long time to digest...
View Article