Determine the number of Elements

**fourth** · Aug 16th 2011, 07:40 AM

HELP!!!!
Let A denote the ideal of Z3[x] generated by the polynomial x^2+x+1, that is,

A={f(x)(x^2+x+1)|f(x) is an element of Z3[x]},

Determine the number of elements in the factor ring Z3[x]/A.

**FernandoRevilla** · Aug 16th 2011, 07:52 AM

Originally Posted by fourth

HELP!!!!Let A denote the ideal of Z3[x] generated by the polynomial x^2+x+1, that is, A={f(x)(x^2+x+1)|f(x) is an element of Z3[x]}. Determine the number of elements in the factor ring Z3[x]/A.

Hint: $p(x)+A=q(x)+A\Leftrightarrow p(x)-q(x)\in A$ . Now use the euclidean division to prove that every element $\mathbb{Z}_3/A$ can be uniquely expressed by $p_1(x)+A$ with $\textrm{deg}(p_1(x))<2$ .

Edited: Of course I meant $\mathbb{Z}_3[x]/A$ instead of $\mathbb{Z}_3/A$ .

Thread: Determine the number of Elements

LinkBack

Thread Tools

Display

Determine the number of Elements

Re: Determine the number of Elements

Similar Math Help Forum Discussions

Determine the number of elements of each order in {C}_{6}x{C}_{3}

Number of Elements of Order 4

Number of elements in a group

Number of elements

number of elements

Search Tags