We know the definition of ED only assume that the existence of an Euclidean function in which Euclidean algorithm works.
My question is: Could we request the Euclidean function is multiplicative in addition?
A question of Euclidean domain
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abstract-algebra
ring-theory
euclidean-domain
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0You mean $f(xy) = f(x)+f(y)$? – 2017-02-24
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0@DustanLevenstein I mean $f(xy)=f(x)f(y)$. – 2017-02-24
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1To my surprise, the answer to this question is unknown, or at least it was as of 2013. See http://math.stackexchange.com/questions/274606/multiplicative-euclidean-function-for-an-euclidean-domain for more – 2017-02-24
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0@AlexWertheim oh... Thanks. – 2017-02-24