Yes you are right there should be a summation sign before aibi, that was my bad. But I have been working with someone else on this problem and we came to the conclusion that, your right, they cannot possibly represent all the ideals of R. But is it possible that they represent all the properties...
Alright, I need some help with this problem (mainly just to get started):
Let A and B be ideals of R, such that:
A+B={a+b / a in A ,b in B}
AB={aibi / ai in A , bi in B}
A:B={x in R / xb in A} are all ideals of R
Show that A+B, AB, and A:B are ALL the ideals of R, where R is a...
For a subgroup H of G and a fixed element a ∈ G,
let H^a = {x∈ G / axa^-1 ∈ H}, it's normalizer N(H) = {a∈G / H^a=H}
Show that for any subgroup H of G, N(H) is a subgroup of G.
I know that for the first one I need to show that closure holds, an identity exists, and inverses exist...