(October 13, 2018 at 6:40 pm)Kernel Sohcahtoa Wrote: I'm most likely going to get back into elementary number theory, as I encountered basic number theory in my study of abstract algebra. Prior to beginning my abstract algebra self-study in early July, I studied divisibility and primes, which IMO, were very interesting. In particular, I enjoyed the proof of the fundamental theorem of arithmetic. Hence, I'm looking forward to learning/getting underneath this material again.
I might suggest learning about Principle Ideal Domains (PIDs). There is a version of the Fundamental Theorem of Arithmetic in that generality, which includes polynomials in one variable. Polynomials in more than one variable are not PIDs, but do also have an analog. They are Unique Factorization Domains (UFDs).