Some accessible treatment of algebraic isomorphisms
Soumyarup Banerjee, Bowen Li, Ruixian Liu, Yu Xin Sun, Shigeru Kanemitsu · Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae Sectio computatorica · 2018
In this note, we unify many well-known theorems in abstract algebra as a result on a principal ideal domain (PID), Theorem 1.3.The proof entails an elucidating argument which establishes several isomorphism theorems in the theory of groups and fields at a stretch.This includes the use of the direct sum to interpret the method of constructing an extension ring of a given ring R as a quotient ring of the polynomial ring over R modulo a non-zero ideal, which in turn includes the case of the ring consisting of degree 0 polynomials as elements of the ring R.