Displaying similar documents to “Hermitian (a,b)-modules and Saito's 'higher residue pairings'”

On the cokernel of the Witt decomposition map

Gabriele Nebe (2000)

Journal de théorie des nombres de Bordeaux

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Let R be a Dedekind domain with field of fractions K and G a finite group. We show that, if R is a ring of p -adic integers, then the Witt decomposition map δ between the Grothendieck-Witt group of bilinear K G -modules and the one of finite bilinear R G -modules is surjective. For number fields K , δ is also surjective, if G is a nilpotent group of odd order, but there are counterexamples for groups of even order.

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.

Périodes évanescentes et (a,b)-modules monogènes

Daniel Barlet (2009)

Bollettino dell'Unione Matematica Italiana

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In order to describe the asymptotic behaviour of a vanishing period in the degeneration of a one parameter family of complex manifolds, we introduce and use a very simple algebraic structure encoding the corresponding filtered Gauss-Manin connection: regular geometric (a,b)-module generated (as left A ~ -modules) by one element. The idea is to use not the full Brieskorn module associated to the Gauss-Manin connection but the minimal (regular) filtered differential equation satisfied by...

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.

On FI-mono-retractable modules

Marziyeh Atashkar, Yahya Talebi (2022)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of FI-mono-retractable modules which is a generalization of compressible modules. We investigate the properties of such modules. It is shown that the rings over which every cyclic module is FI-mono-retractable are simple Noetherian V -ring with zero socle or Artinian semisimple. The last section of the paper is devoted to the endomorphism rings of FI-retractable modules.

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.

Estimates of global dimension

Wei Jiaqun (2006)

Czechoslovak Mathematical Journal

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In this note we show that for a * n -module, in particular, an almost n -tilting module, P over a ring R with A = E n d R P such that P A has finite flat dimension, the upper bound of the global dimension of A can be estimated by the global dimension of R and hence generalize the corresponding results in tilting theory and the ones in the theory of * -modules. As an application, we show that for a finitely generated projective module over a VN regular ring R , the global dimension of its endomorphism ring...

Wakamatsu tilting modules with finite injective dimension

Guoqiang Zhao, Lirong Yin (2013)

Czechoslovak Mathematical Journal

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Let R be a left Noetherian ring, S a right Noetherian ring and R ω a Wakamatsu tilting module with S = End ( R ω ) . We introduce the notion of the ω -torsionfree dimension of finitely generated R -modules and give some criteria for computing it. For any n ≥ 0 , we prove that l . id R ( ω ) = r . id S ( ω ) ≤ n if and only if every finitely generated left R -module and every finitely generated right S -module have ω -torsionfree dimension at most n , if and only if every finitely generated left R -module (or right S -module) has generalized Gorenstein...