Every finite integral domain is isomorphic to Zp Prove or disprove

Corinne Woods

Corinne Woods

Open question

2022-08-29

Every finite integral domain is isomorphic to Zp
Prove or disprove

Answer & Explanation

Nezveda6q

Nezveda6q

Beginner2022-08-30Added 7 answers

Let F be a field with p elements where p is prime. By Lagrange, the order of e must divide p. Thus the order of e is p. In other words, char F = p. Since F is a field it is an integral domain, thus by theorem 6.18 there exists a subring R of F, such that R = Zp. Thus R must have p elements, hence R = F. Thus F= Zp.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?