Let R be a filtered Noetherian ring with identity and M an R-filtered module. The associated graded ring of R is denoted by G(R) and the associated graded G(R) module of M is denoted by gr(M). Bjork studied in ref. [1...Let R be a filtered Noetherian ring with identity and M an R-filtered module. The associated graded ring of R is denoted by G(R) and the associated graded G(R) module of M is denoted by gr(M). Bjork studied in ref. [1] the relation between M being a module with a good filtration and gr(M) being a finitely generated module. If R is a ring with positive filtration and G(R) is a Noetherian ring, then M is a module with good filtration if and only if gr(M) is a finitely generated G(R) module. But when R is a Zariski filtered ring,we do not know if the conclusion is true. To be specific, Bjork’s problem is:展开更多
In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated...In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.展开更多
文摘Let R be a filtered Noetherian ring with identity and M an R-filtered module. The associated graded ring of R is denoted by G(R) and the associated graded G(R) module of M is denoted by gr(M). Bjork studied in ref. [1] the relation between M being a module with a good filtration and gr(M) being a finitely generated module. If R is a ring with positive filtration and G(R) is a Noetherian ring, then M is a module with good filtration if and only if gr(M) is a finitely generated G(R) module. But when R is a Zariski filtered ring,we do not know if the conclusion is true. To be specific, Bjork’s problem is:
文摘In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
