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Last edited by Hom on Sun Oct 16, 2011 9:35 am, edited 1 time in total.

(1) and (3):

(2) is not in the ideal because you cannot get an x by multiplying or adding/subtracting powers of x^2 and x^3.

(2) is not in the ideal because you cannot get an x by multiplying or adding/subtracting powers of x^2 and x^3.

Thanks owlpride.

Last edited by Hom on Sun Oct 16, 2011 9:38 am, edited 2 times in total.

Since is a multiple of 2, it is congruent to zero mod 2, so you get .

The elements work the same way in as they do for any other polynomial ring. The construction of ensures that is never an element of , so it will behave the same way regardless of the choice of .

That makes prefect sense to me now. Thank you so much for the explanation.

Btw, do you guys know any good problem sets/practices for abstract algebra and general topology? I really think they can get a beginner like me into thinking various problems and getting a better understanding.

Btw, do you guys know any good problem sets/practices for abstract algebra and general topology? I really think they can get a beginner like me into thinking various problems and getting a better understanding.

Last edited by Hom on Sun Oct 16, 2011 9:37 am, edited 1 time in total.

You realize it is against the rules to post this question at all, right?

goombayao wrote:You realize it is against the rules to post this question at all, right?

Sorry, I was not aware of that but I am now. I've removed the content.

^^tattle-tail. WHO CARES.

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