## Notes

### A Compendium on Basic Commutative Ring Structures

Abstract: It seems that a majority of my undergraduate algebra career was spent trying to prove inclusions, mutual intersections,…

### Visualizing Simplicial Objects

Definition. Let $[n]$ denote the set $\{0,1,\dots,n\}$. We define the category $\Delta\subseteq \mathcal{Set}$ (called the category of combinatorial simplices)…

### Failure of the Hahn-Banach in ℂₚ

The Hahn-Banach is known to be a crucial tool in functional analysis. The following are lecture notes written…

## Exercises

### Exercises #6 – Climbing Algebraic Topology – #4

As a reference, we permit the use of homotopy theorems established in Topology and Geometry [Bredon1993] up till…

### Exercises #6 – Climbing Algebraic Topology – #3

We use some of the results established in Topology and Geometry [Bredon1993] implicitly. In particular, the fact that…

### Exercises #5 – Augmentation Ideal

Definition. For any group $G$, the augmentation map of the group ring $\mathbb{Z} G$ is defined to be…