Hermitian (a,b)-modules and Saito's

Piotr P. Karwasz

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 $R = Z ₂ (R_{R}) \oplus R^{'}$ , where R’ is a hereditary right R-module. Examples illustrating the results are presented.

Filtrations on generalized Verma modules for Hermitian symmetric pairs.

R.S. Irving, D.A. Collingwood (1988)

Journal für die reine und angewandte Mathematik

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Extensions Between Generalized Verma Modules: The Hermitian Symmetric Cases.

Brad Shelton (1988)

Mathematische Zeitschrift

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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 $\widetilde{A}$ -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...

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...

Hermitian forms on link modules.

M. Farber (1991)

Commentarii mathematici Helvetici

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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 $n \geq 0$ , we prove that ${l . id}_{R} (ω) = {r . id}_{S} (ω) \leq n$ 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...

The Hermitian Morita theorems.

Verhaege, P., Verschoren, A. (1998)

Divulgaciones Matemáticas

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

$k$ -torsionless modules with finite Gorenstein dimension

Maryam Salimi, Elham Tavasoli, Siamak Yassemi (2012)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative Noetherian ring. It is shown that the finitely generated $R$ -module $M$ with finite Gorenstein dimension is reflexive if and only if $M_{𝔭}$ is reflexive for $𝔭 \in Spec (R)$ with $depth (R_{𝔭}) \leq 1$ , and ${G- dim}_{R_{𝔭}} (M_{𝔭}) \leq depth (R_{𝔭}) - 2$ for $𝔭 \in Spec (R)$ with $depth (R_{𝔭}) \geq 2$ . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for $n \geq 2$ we give a characterization of $n$ -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally...