ideals

We prove that Z is universal in the category of rings with identity. Using that, we define the characteristic of a field, and prove that it is well-defined. We then discuss ring ideals a bit more before finishing by showing that all fields with exactly p elements (where p is prime) are isomorphic.

In this entry, we define the sum and product of two ring Ideals. We then prove the Chinese Remainder Theorem for Ideals. Along the way, we study a tiny bit of Category theory, enough to define free objects and work a little bit with free rings.

In this entry we introduce rings and fields. We establish some of their basic properties.