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-   -   Multiplicative inverse in factor ring? (http://mymathforum.com/abstract-algebra/42818-multiplicative-inverse-factor-ring.html)

ricsi046 April 12th, 2014 12:27 AM

Multiplicative inverse in factor ring?
 
Hello,
can someone tell me how to find the multiplicative inverse of an element in a factor ring?
Let the element be f and the factor ring T[x]/(m).
The basic idea is to solve a diophantine equation like f*u-m*v=1,right?and we need to find u

Olinguito April 12th, 2014 04:03 AM

You have the right idea – except that an element of $T[x]/(m)$ is of the form $f+(m)$ where $f$ is a polynomial of degree at most $\deg(m)-1$. When you have found a polynomial $u$ such that $fu=1+mv$ for some polynomial $v$, the multiplicative inverse of $f+(m)$ will be $u+(m)$.

ricsi046 April 12th, 2014 04:05 AM

i see,thanks


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