Let w = 2/3 = -1+i3, let R = Z[w]. Let p be a positive ==...

 

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Let w = 2/3 = -1+i3, let R = Z[w]. Let p be a positive == prime integer which is not equal to 3. (a) Prove that R is an Euclidean domain, and find all the units of R. (b) Prove that the ideal pR is a maximal ideal of R, if and only if, p = 1 (modulo 3). Let w = 2/3 = -1+i3, let R = Z[w]. Let p be a positive == prime integer which is not equal to 3. (a) Prove that R is an Euclidean domain, and find all the units of R. (b) Prove that the ideal pR is a maximal ideal of R, if and only if, p = 1 (modulo 3).

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a Proving R is a Euclidean Domain and Finding Units R is a Subring of Complex Numbers R Zw is the ri... View the full answer