Abstract algebra

Q&ACategory: MathematicsAbstract algebra
Abir rangan DattaAbir rangan Datta asked 5 years ago

How to show a integral domain with finite number of ideals is a field ??

2 Answers
sanket dutta answered 4 days ago

let R be your integral domain, and suppose α∈R is nonzero. Consider the ideals ⟨α⟩,⟨α^2⟩,⟨α^3⟩,… and since R has finite number of ideals so there must exist some k1 and k2 such that =.
I think after this the rest part is obvious.

sanket dutta answered 4 days ago

such that a^k1 = a^k2 

Your Answer

1 + 3 =