6.1

1. What was the most difficult part of the reading for you?
I think that I can follow the concept of ideals pretty well. It seems to make sense to me, and that is good. The thing that I'm struggling with, and it could be my level of focus, is the distinction between the different ideals that the book talks about.

2. Write the definitions of the different ideals:
IDEAL: A subring I of a ring R is an ideal provided that whenever r in R and a in I, then ra in I and ar in I. Note, a nonempty subset I of a ring R is an ieal if and only if it has these properties: i) if a,b in I, then a-b in I; ii) if r in R and a in I, then ra in I and ar in I.

LEFT IDEAL: Like the fourth example on page 136 -- like a matrix that seems to have an ideal for ra but maybe not for ar.

PRINCIPAL IDEAL GENERATED BY C: Let R be a commutative ring with identity, c in R and I the set of all multiples of c in R, that is, I={rc | r in R}. Then I is and ideal. (yeah, I still don't really get this)

IDEALS GENERATED BY C1, C2,...., CN: Let R be a commutative ring with identity and c1, c2,....,cn in R. Then the set I={r1c1+r2c2+....+rncn|r1, r2,....,rn in R} is an ideal in R. (again.... I don't really see it.)