John A. Beachy, Christine M. Leroux
Abstract
It is shown that prime ideals of a Noetherian ring are linked if and only if certain corresponding prime ideals are linked in an associated Artinian ring. Furthermore, it is shown that there is a canonical linking ideal, which can be found by using a construction based on middle annihilator ideals.
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It is shown that prime ideals of a Noetherian ring are linked if and only if certain corresponding prime ideals are linked in an associated Artinian ring. Furthermore, it is shown that there is a canonical linking ideal, which can be found by using a construction based on middle annihilator ideals.
Key concepts: Mathematics, Associated prime, Artinian ring, Radical of a ring, Annihilator, Semiprime ring, Semisimple module, Noetherian