Solution Found!
Let d be an integer. Prove that is an integral domain.
Chapter 13, Problem 11E(choose chapter or problem)
QUESTION:
Let d be an integer. Prove that \(Z[\sqrt d] = \{a + b \sqrt d | a, b \in Z\}\) is an integral domain. (This exercise is referred to in Chapter 18.)
Questions & Answers
QUESTION:
Let d be an integer. Prove that \(Z[\sqrt d] = \{a + b \sqrt d | a, b \in Z\}\) is an integral domain. (This exercise is referred to in Chapter 18.)
ANSWER:Step 1 of 7
Let d be an integer. To prove is an integral domain, argue as follows.
Consider two cases