1.Describe the field F of quotients of the integral subdomain D={n+m√2|n,m∈Z}of R.
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2.Decide whether the indicated operations of addition and multiplication are defined (closed) on the set, and give a fing structure. If a ring is not formed, tell why this is the case. If a ring is formed, state whether the ring is commutative, whether it has unity, and whether it is a field.
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PROBLEM){a+b√2|a,b∈Z} with the usual addition and multiplication.
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이 두문제 인데요...꼭 좀 풀어주세요...ㅠㅠ
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첫댓글 1. D = { n+m√2 | n,m∈Z }=Z[√2] 의 the field F of quotients 는 Q(√2) = { n+m√2 | n,m∈Q } 입니다.
2. Z[√2] 는 유클리드 정역이 됩니다.