More on rings: https://en.wikipedia.org/wiki/Ring_(mathematics).
The detailed proof of Fermat’s Last Theorem for regular primes can be found in a very well-written article by Keith Conrad: https://kconrad.math.uconn.edu/blurbs/gradnumthy/fltreg.pdf.
...And another good source: http://www.math.columbia.edu/~ila/Kummer.pdf.
The original approach by Lamé (which outlines an overall erroneous proof but nevertheless provides the valuable decomposition of the left side of the Fermat’s equation; in French): https://gallica.bnf.fr/ark:/12148/bpt6k29812/f310.item.zoom.
...And English commentary to the article above: https://math.stackexchange.com/questions/953462/what-was-lames-proof.
An interesting thread on (non-)unique factorization in cyclotomic rings of integers: https://math.stackexchange.com/questions/85520/fermats-last-theorem-and-kummers-objection.
Overview of progression on Fermat’s Last Theorem over time: https://en.wikipedia.org/wiki/Fermat's_Last_Theorem.
More on regular and irregular primes: https://en.wikipedia.org/wiki/Regular_prime.
The Fundamental Theorem of Algebra: https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra.