[代數] unique factorization domain

[TampaBayRays (坦帕灣光芒)]

1.Find a unique factorization domain D and let d is an irreducible element

in D and let d belong to D such that d is an irreducible element in D but

D/<d> is not a field.

2.Let D be a ED with Euclidean valuation v:D\{0}→N∪{0}

  Let I be a nontrivial ideal of D and let a belong to I be a nonzero element

  prove that: I=<a> iff v(a) = min{v(b)|b belong to I\{0}}

請版上的各位高手們幫我解答~

謝謝!!!

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◆ From: 114.43.146.151
※ 編輯: TampaBayRays    來自: 114.43.146.151       (11/12 01:49)
推 yusd24      :雖然我看不太懂題目  但是 D=Z[x,y], d=x應該可以