A commutative ring $R$ with identity is said to be coherent if every f.g. ideal of $R$ is f.p. We know that any noetherian ring is coherent. A Laskerian ring is a ring in which every ideal has a primary decomposition. Now, Is any Laskerian ring coherent?
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1 Answer
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Even strongly Laskerian rings are not necessarily coherent.
By a theorem of Radu strongly Laskerian coherent rings are Noetherian, and there are examples of strongly Laskerian rings which are not Noetherian.
