Chapter 4 Factor Rings

Question 1

What is the factor ring of R by I

Answer 1

Let R be a ring and I be a proper Ideal Let R/I denote the set of cosets of I in
R/I={r+I | r in R}

Question 2

When is an ideal maximum?

Answer 2

An ideal Iof R is maximal if it is proper and for any ideal J with I≤ J ≤ R we have J=I or J=R

Question 3

What is a prime ideal?

Answer 3

Let R be a commutative ring and let I be a proper Ideal,we say that I is a prime ideal if whenever r,s in R and rs in I then either r in I or s in I