Hi Guys ;

how many elements are in $\displaystyle \mathbb Z_5[i]/<1+i>$ ?

(Itwasntme)

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- May 16th 2009, 07:21 AMleonardo1000The number of elements in Gaussian Factor ring
Hi Guys ;

how many elements are in $\displaystyle \mathbb Z_5[i]/<1+i>$ ?

(Itwasntme) - May 16th 2009, 08:37 AMSwlabr

How many elements are in $\displaystyle \mathbb Z_5[i]$? What about $\displaystyle <1+i>$? Clearly, $\displaystyle \mathbb Z_5[i]$ has 25 elements, so $\displaystyle <1+i>$ has either 1, 5 or 25 elements. It's not got only 1 element, obviously (as it contains 0). I'll leave the rest of that bit to you...and the solution to your problem is simply $\displaystyle |\mathbb Z_5[i]|/|<1+i>| = 25/|<1+i>|$. - May 16th 2009, 01:33 PMNonCommAlg