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, and reformulations of different commutative ring structures. In this short story, I will attempt to provide a compendium of equivalency theorems, properties, and other elements of commutative algebra. The pedagogy here is purposefully unmotivating; you can probably find some motivation on Wikipedia or among other sources, however I contend these are not the best sources and encourage looking at them for finding references only.

I complete this as I feel. All proofs are internal to this document implying any accessory lemmas are placed in the Appendix. The level of accessory is kind of arbitrary, but reading the current version will give a good hint of the standard I use.

If you would like to give corrections or provide proofs, please email me at university@jeongjh.com. Do not reference books or webpages; if I did this, there would be no point in writing this. The proofs should solely be yours and I will only take TeXed documents. Creative and short solutions are given priority over long and pedagogical ones.


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