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Coherence relative to a weak torsion class

Zhanmin Zhu (2018)

Czechoslovak Mathematical Journal

Let R be a ring. A subclass 𝒯 of left R -modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let 𝒯 be a weak torsion class of left R -modules and n a positive integer. Then a left R -module M is called 𝒯 -finitely generated if there exists a finitely generated submodule N such that M / N ∈ 𝒯 ; a left R -module A is called ( 𝒯 , n ) -presented if there exists an exact sequence of left R -modules 0 ⟶ K n - 1 ⟶ F n - 1 ⟶ ⋯ ⟶ F 1 ⟶ F 0 ⟶ M ⟶ 0 such that F 0 , ⋯ , F n - 1 are finitely generated free and K n - 1 is 𝒯 -finitely generated; a left R -module...

Cohomologie locale de certains anneaux Auslander-Gorenstein.

Marie-Paule Malliavin (1992)

Publicacions Matemàtiques

We give axiomatic conditions in order to calculate the local cohomology of some idempotent kernel functors. These results lie in some new dimension introduced by T. Levasseur for Auslander-Gorenstein rings. Under some hypothesis, we generalize previous results.

Complexity and periodicity

Petter Andreas Bergh (2006)

Colloquium Mathematicae

Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when...

C(X) vs. C(X) modulo its socle

F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)

Colloquium Mathematicae

Let C F ( X ) be the socle of C(X). It is shown that each prime ideal in C ( X ) / C F ( X ) is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that d i m ( C ( X ) / C F ( X ) ) ≥ d i m C ( X ) , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...

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