- define ring, integral domain and characteristic of an integral domain, solve examples and prove related theorems.
- define subring and ideal, solve examples and prove related theorems.
- define quotient ring, solve examples and prove related theorems
- define principal ideal domain, solve examples and prove related theorems.
- define homomorphism and isomorphism, solve examples and prove related theorems.
- define polynomials and polynomial rings, solve examples and prove related theorems.
- learn how a polynomial is splitted into the prime factors, solve examples.
- define maximaland prime ideal, solve examples and prove related theorems.