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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 [latex][n][/latex] denote the set [latex]\{0,1,\dots,n\}[/latex]. We define the category [latex]\Delta\subseteq \mathcal{Set}[/latex] (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 [latex]G[/latex], the augmentation map of the group ring [latex]\mathbb{Z} G[/latex] is defined to be…