Abstract Algebra Answers

Using Cayley’s theorem, find the permutation group to which a cyclic group of 

order 12 is isomorphic.

Prove that every finite ring is noetherian.

Write ten examples of Extension field?

Prove that rational numbers is a smallest infinite field?

Show that pZ is a prime ideal of Z for all primes p.

Prove that every field is artinian.Deduce that Q is artinian.

Prove that every finite ring is artinian.

Find the solution of the equation x³-2x²-3x in z₁₂

Find the solution of the equation x³-2x²-3x in z₁₂