Displaying similar documents to “On finitely generated multiplication modules”

Artinian cofinite modules over complete Noetherian local rings

Behrouz Sadeghi, Kamal Bahmanpour, Jafar A'zami (2013)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R -module. In this paper it is shown that if 𝔭 is a prime ideal of R such that dim R / 𝔭 = 1 and ( 0 : M 𝔭 ) is not finitely generated and for each i ≥ 2 the R -module Ext R i ( M , R / 𝔭 ) is of finite length, then the R -module Ext R 1 ( M , R / 𝔭 ) is not of finite length. Using this result, it is shown that for all finitely generated R -modules N with Supp ( N ) ⊆ V ( I ) and for all integers i ≥ 0 , the R -modules Ext R i ( N , M ) are of finite length, if and only if, for all finitely generated R -modules...

Multiplication modules and related results

Shahabaddin Ebrahimi Atani (2004)

Archivum Mathematicum

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Let R be a commutative ring with non-zero identity. Various properties of multiplication modules are considered. We generalize Ohm’s properties for submodules of a finitely generated faithful multiplication R -module (see [8], [12] and [3]).

⊕ -cofinitely supplemented modules

H. Çalışıcı, A. Pancar (2004)

Czechoslovak Mathematical Journal

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Let R be a ring and M a right R -module. M is called ⊕ -cofinitely supplemented if every submodule N of M with M N finitely generated has a supplement that is a direct summand of M . In this paper various properties of the ⊕ -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of ⊕ -cofinitely supplemented modules is ⊕ -cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R -module is ⊕ -cofinitely supplemented. In addition, if M has the...

Some results on the cofiniteness of local cohomology modules

Sohrab Sohrabi Laleh, Mir Yousef Sadeghi, Mahdi Hanifi Mostaghim (2012)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring, 𝔞 an ideal of R , M an R -module and t a non-negative integer. In this paper we show that the class of minimax modules includes the class of 𝒜ℱ modules. The main result is that if the R -module Ext R t ( R / 𝔞 , M ) is finite (finitely generated), H 𝔞 i ( M ) is 𝔞 -cofinite for all i < t and H 𝔞 t ( M ) is minimax then H 𝔞 t ( M ) is 𝔞 -cofinite. As a consequence we show that if M and N are finite R -modules and H 𝔞 i ( N ) is minimax for all i < t then the set of associated prime ideals of the generalized local cohomology...