Displaying similar documents to “Périodes évanescentes et (a,b)-modules monogènes”

Commutative rings whose certain modules decompose into direct sums of cyclic submodules

Farid Kourki, Rachid Tribak (2023)

Czechoslovak Mathematical Journal

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We provide some characterizations of rings R for which every (finitely generated) module belonging to a class 𝒞 of R -modules is a direct sum of cyclic submodules. We focus on the cases, where the class 𝒞 is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.

T-Rickart modules

S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pish Hesari (2012)

Colloquium Mathematicae

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We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that R is right Σ-t-extending if and only if every R-module is T-Rickart. Also, every free R-module is T-Rickart if and only if R = Z ₂ ( R R ) ⊕ R ' , where R’ is a hereditary right R-module. Examples illustrating the results are presented.

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...

⊕ -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...

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

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We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between n -Gorenstein star modules and n -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of n -Gorenstein tilting modules.

Some results on the local cohomology of minimax modules

Ahmad Abbasi, Hajar Roshan-Shekalgourabi, Dawood Hassanzadeh-Lelekaami (2014)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring with identity and I an ideal of R . It is shown that, if M is a non-zero minimax R -module such that dim Supp H I i ( M ) ≤ 1 for all i , then the R -module H I i ( M ) is I -cominimax for all i . In fact, H I i ( M ) is I -cofinite for all i ≥ 1 . Also, we prove that for a weakly Laskerian R -module M , if R is local and t is a non-negative integer such that dim Supp H I i ( M ) ≤ 2 for all i < t , then Ext R j ( R / I , H I i ( M ) ) and Hom R ( R / I , H I t ( M ) ) are weakly Laskerian for all i < t and all j ≥ 0 . As a consequence, the set of associated primes of H I i ( M ) is finite for all i ≥ 0 , whenever...

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma (2024)

Czechoslovak Mathematical Journal

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We construct a family of non-weight modules which are free U ( 𝔥 ) -modules of rank 2 over the N = 1 super Schrödinger algebra in ( 1 + 1 ) -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free U ( 𝔥 ) -modules of rank 2 over 𝔬𝔰𝔭 ( 1 | 2 ) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.