# Answer to Question #3101 in Abstract Algebra for marwa

Question #3101

1. Find the quotient and the remainder upon dividing 4 + 9i by 3 + i in Z[i].

2.& Determine whether the polynomial& x

3.& Let F be a field and let p(x) ∈ F[x]. Show that p(x) is irreducible if and only if < p(x)> is maximal.

4.& Consider the ring R = and let p ∈ R. Prove or give a counter example that < p> is prime implies is maximal?

2.& Determine whether the polynomial& x

^{4}- x^{3}- x + 2 is irreducible in Z_{3}[x]. If not, factor the polynomial completely3.& Let F be a field and let p(x) ∈ F[x]. Show that p(x) is irreducible if and only if < p(x)> is maximal.

4.& Consider the ring R = and let p ∈ R. Prove or give a counter example that < p> is prime implies is maximal?

Expert's answer

Unfortunately, your question requires a lot of work and cannot be done for free. Submit it with all requirements as an assignment to our control panel and we'll assist you.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment