Question: Let w = 2/3 = -1+i3, let R = Z[w]. Let p be a positive == prime integer which is not equal to 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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