We define ring homomorphisms in this lecture and talk abou some examples, more emphasis on substitution homomorphisms for polynomial rings.
Next we talk about the correspondence theorem and the isomorphism theorems for ring homomorphisms.
CORRECTION: In order to form the quotient ring R/I, I has to be a both sided ideal. In fact, while establishing the well-definedness of the product rule (a+I)(b+I)=ab+I, one can see that it is necessary to take I to be a both sided ideal. By mistake, it has been wrongly conveyed in the lecture that the collection of cosets R/I can be given the ring structure in the natural way when I is just a left ideal. This is certainly not true. Indeed, kernel o a ring homomorphism is a both sided ideal.
