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Note on a new class of filtrations on rings and modules
Epiphane Pascal TOGBE and Daouda SANGARÉ
Université Nangui Abrogoua, UFR SFA,
Laboratoire de Mathématiques et Informatique
Mathematics Subject Classification: 13A02, 13A30, 13J30, 16W50, 16W70 .
Key words: filtrations, f -good (resp. f -fine) filtration, T- good (resp. T- fine)
filtration, Rees modules of filtrations
Abstract:
Here we introduce the concept of T-good and T -fine filtration on an A-module M with respect to a given filtration f on a commutative ring A and we investigate some properties of those filtrations, namely in comparison with f-good and f-fine filtrations on modules as introduced by Okon and Ratliff,Jr in [OR], As a counter example, we give a filtration which is T-fine but not T-good. We end this paper by stating a Theorem which gives, under mild conditions, a criterion for a filtration F on the A-module M to be T-fine with respect to a given filtration f on A, in terms of the Rees module of F with respect to M and the Rees ring of f.