Hi!
I have problem with this exercice
Find three ideals in with thr property that ( means is a proper subsets of)
- Definition
An ideal in a commutative ring is a subset of such that
If , then
I think of and but are not ideal since fails
First, you mean " " rather than " ", don't you? (2), (4), and (6) are the sets of all multiples of 2, 4, and 6, respectively, right? Then it certainly is true that "if a and b in I then a+ b in I". if a and b are multiples of r, then a= mr, and b= nr so a+ b= mr+ nr= (m+ n)r.
This is in your original
Now you post:
So we are rightly confused as to what you do understand. Do you see why that is?
Surely you are not saying that you do not understand the notation: $B\subsetneq A~?$
If you do not understand the notation it means: $[B\subset A] \wedge[\exists x\in A$ such that $x\notin B]$
If you know what $(24)$ is then is it true that $(24)\subsetneq (4)~?$
You mean . But yes, that is , all multiples of 4. Those dots of course, mean that it continues in that way- it also contains -24= 4(-6), 24= 4(6), -48= 4(-12), 48= 4(12), etc.
consists of all multiples of 24 which are all multiples of 4 because 24 itself is a multiple of 4.but I do not understand this condition
Similarly, which, again, contains all multiples of 24 because 24 is a multiple of 6.
The ideals (2) (4) and (6) satisfy the condition ?