Ideals and Quotient Rings
Definition of Ideal
Principal Ideals
Examples
Example 1: is an ideal of , and every ideal of is principal.
Example 2: has no non-trivial ideals (simple ring).
Example 3: The set of polynomials of degree is not an ideal (not closed under addition).
Quotient Ring
Properties
First Isomorphism Theorem for Rings
Prime Ideals
Maximal Ideals
Key Results
Chinese Remainder Theorem
Application to
For :