We know from elementary ring theory that in a principal ideal domain, every ideal is generated by one element, and nonzero prime ideals are maximal. We also know that a typical example of a principal ideal domain is the ring k[x], where k is a field. I am going to define a general concept of dimension for a ring, such that k[x1, x2, ..., x(n)] has dimension n, and such that principal ideal domains and rings with similar properties have dimension 1.
The talk should be accessible to everybody (elementary algebra required).