- Thread starter
- #1

- Jun 22, 2012

- 2,918

In the proof I is an ideal in R[x] L is the set of all leading coefficients of elements of I

D&F then proceed to prove that L is an ideal of R

Basically they establish that if elements a and b belong to L and r belongs to L then ra - b belongs to L.

D&F claim that this shows that L is an ideal but for an ideal we need to show that for [TEX] a, b \in L [/TEX] and [TEX] r \in R[/TEX] we have:

[TEX] a - b \in L [/TEX] and [TEX] ra \in R [/TEX]

My question is how exactly does [TEX] ra - b \in L \Longrightarrow a - b \in L [/TEX] and [TEX] ra \in R [/TEX]??

Peter

[This has also been posted on MHF]