Let r be an euclidean domain with degree function

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1. Let R be an Euclidean domain with degree function ? and R is not a ?eld.

(1) Let a is not equal 0 and b is not equal 0 be two elements in R. Suppose that a|b and b is not divide a. Prove that ?(a) is smaller than ?(b).

(2) Suppose that ?(ab) = ?(a)?(b), for all a,b ∈ R {0}. Prove that an element u ∈ R is a unit if and only if ?(u) = 1.

Reference no: EM13718765

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