⚠ Note: These posts were originally written as personal study notes for my own reference. They may contain errors or inaccuracies — please read with appropriate skepticism.
On Quasi-finite Morphisms (Part 2)
In this post, we continue our discussion of the application of Zariski's Main Theorem, following 'On Quasi-finite Morphisms (Part 1)'.
On Quasi-finite Morphisms (Part 1)
In this post, we will discuss the definition and properties of quasi-finite morphisms, and its application to Zariski's Main Theorem.
On the Characteristic of a Ring
In this post, we will see that the usual definition of the characteristic of a ring obscures its true nature, and explain why another equivalent characterization is conceptually more useful.
Algebraically closed complete field may not have a complete image in $\mathbb{R}$ under its absolute value
In this post, we will see that the image of $\mathbb{C}_p$, the complete algebraic closure of $\mathbb{Q}_p$, has a non-complete image in $\mathbb{R}$.
Natural Isomorphisms with Non-Natural-Looking Inverses
In this post, we will talk about canonical isomorprhisms with non-canonical-looking inverses related to tensor products in linear algebra.