2 X is not a principal ideal
「2 X is not a principal ideal」熱門搜尋資訊
「2 X is not a principal ideal」文章包含有：「(2」、「1CHAPTER3」、「ExampleofanidealwhichisnotprincipalintheringZ[x]...」、「Is$mathbbZ}[x]$aprincipalidealdomain?」、「IsI=⟨5」、「Proofverification:⟨2」、「Provethat(2」、「Provingthatanidealisnotaprincipalideal」、「⟨2,x⟩isanon」
查看更多
(2
https://math.stackexchange.com
Suppose that (2,x)=(p), this implies that 2=pq this implies that p and q are constant and p divides 2. Since (2,x)≠Z[X], p=2.
1 CHAPTER 3
https://people.math.carleton.c
Solution. Suppose that the ideal I =< 2,X > in Z[X] is principal. Then there exists f(X) ∈ Z[X] such that I =< f(X) >. As 2 ∈ I there exists.
![Example of an ideal which is not principal in the ring Z[x] ...](https://api.multiavatar.com/Example+of+an+ideal+which+is+not+principal+in+the+ring+Z%5Bx%5D+....png?apikey=viVnb6N20jclO8){kind=avatar}
Example of an ideal which is not principal in the ring Z[x] ...
https://math.stackexchange.com
Try the following one: I=⟨2,x⟩≤Z[x] . Try first to characterize the elements of the ideal (take a good peek at the free coefficient of ...
![Is $mathbbZ}[x]$ a principal ideal domain?](https://api.multiavatar.com/Is+%24mathbbZ%7D%5Bx%5D%24+a+principal+ideal+domain%3F.png?apikey=viVnb6N20jclO8){kind=avatar}
Is $mathbbZ}[x]$ a principal ideal domain?
https://math.stackexchange.com
No. Consider the ideal (2,x). In general, ...
Is I=⟨5
https://math.stackexchange.com
1 Answer 1 ... Z[X]/⟨5,X⟩≅Z5 is a field so ⟨5,X⟩ is a prime ideal (it is even maximal). On the other hand, note that Z[X]/⟨2,X2⟩≅Z2[X]/(X2) ...
Proof verification: ⟨2
https://math.stackexchange.com
I want to prove that ⟨2,x⟩ is a prime, but not principal, ideal of Z[X]. ⟨2,x⟩ is prime: Suppose f(x)=fnxn+…+f1x+f0 and g(x)=gmxm+…
Prove that (2
https://www.epsilonify.com
Proof. Assume by contradiction that ( 2 , x ) (2,x) (2,x) is a principal ideal. Then ( 2 , x ) = ( f ( x ) ) (2,x) = (f(x)) (2,x)=(f(x)), where ...
Proving that an ideal is not a principal ideal
https://math.stackexchange.com
1 Answer 1 ... You correctly state that A(X) should be a common factor of 2 and X. However the two facts you deem “obvious” aren't. Not difficult, ...
⟨2,x⟩ is a non
https://math.stackexchange.com
Therefore, we conclude that (2,X) can never be a principal ideal of Z[X]. Share.