Abstract
If there exists a finitely generated module M over a t-ring such that tM=AnnMt and M/tM is of finite length, then we show that commutator ideal [q,q] is contained in tq, for some prime ideal q under certain conditions. Using this property, we discuss the Noetherian property of the Rees algebra of the prime ideal q in t-ring and as an application we give an analogue of the Artin–Rees lemma for t-rings.
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