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Sketch 2

Examples of rings and their properties


Huh...

it seems like rings are super interesting, and I still don't know them like the back of my hand. That's why this sketch is dedicated to them.

Date Started: January 16, 2024
Date Finished: Unfinished

A list of rings to consider...

I studied much of what I know about algebra from Dummit and Foote as well as Lang and Matsumura, so many of the examples I will think of were inspired by these sources (and my algebra professors). If anyone has other ideas of useful rings to consider, contact me, I would love to learn to sketch them.

Integers, Rational Numbers, Real Numbers
Ring of Entire Functions
Polynomials
Residuals mod n
Matrices

Infinite Rings

Integers, Rational Numbers, Real Numbers

The integers, rationals and reals which I discussed in Sketch 1 as being nice abelian groups are also rings (and in a future sketch I guess I will also mention that they are fields), with multiplication being well known.

Ring of Entire Functions

Integers