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I am looking for an example of a primary decomposition of an ideal in a commutative noetherian ring, that isn't an UFD nor a dedekind domain and where the primary ideals in the decomposition is not equal to there radical ideals. That is, a good example on how to use the theory of existence and uniqueness of primary decomposition in Noetherian rings.

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    see http://math.stackexchange.com/questions/834673/decomposition-of-i-x2-y2-xy#8346732014-06-15

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