Spectral properties of quotients of Beurling-type submodules of the Hardy module over the unit ball

Kunyu Guo; Yongjiang Duan

Displaying similar documents to “Spectral properties of quotients of Beurling-type submodules of the Hardy module over the unit ball”

On generalized CS-modules

Qingyi Zeng (2015)

Czechoslovak Mathematical Journal

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An $𝒮$ -closed submodule of a module $M$ is a submodule $N$ for which $M / N$ is nonsingular. A module $M$ is called a generalized CS-module (or briefly, GCS-module) if any $𝒮$ -closed submodule $N$ of $M$ is a direct summand of $M$ . Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right $R$ -modules are projective if and only if all right $R$ -modules are GCS-modules.

Derived dimension via $τ$ -tilting theory

Yingying Zhang (2021)

Czechoslovak Mathematical Journal

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Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support $τ$ -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given $τ$ -tilting module.

Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi (2017)

Czechoslovak Mathematical Journal

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Let $R$ be a commutative Noetherian ring and let $C$ be a semidualizing $R$ -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to $C$ which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every $G_{C}$ -injective module $G$ , the character module $G^{+}$ is $G_{C}$ -flat, then the class ${𝒢ℐ}_{C} (R) \cap 𝒜_{C} (R)$ is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class ${𝒢ℐ}_{C} (R) \cap 𝒜_{C} (R)$ ...

Characterizations of incidence modules

Naseer Ullah, Hailou Yao, Qianqian Yuan, Muhammad Azam (2024)

Czechoslovak Mathematical Journal

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Let $R$ be an associative ring and $M$ be a left $R$ -module. We introduce the concept of the incidence module $I (X, M)$ of a locally finite partially ordered set $X$ over $M$ . We study the properties of $I (X, M)$ and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.

Subsets of nonempty joint spectrum in topological algebras

Antoni Wawrzyńczyk (2018)

Mathematica Bohemica

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We give a necessary and a sufficient condition for a subset $S$ of a locally convex Waelbroeck algebra $𝒜$ to have a non-void left joint spectrum $σ_{l} (S) .$ In particular, for a Lie subalgebra $L \subset 𝒜$ we have $σ_{l} (L) \neq \emptyset$ if and only if $[L, L]$ generates in $𝒜$ a proper left ideal. We also obtain a version of the spectral mapping formula for a modified left joint spectrum. Analogous theorems for the right joint spectrum and the Harte spectrum are also valid.

On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence

Kosar Abolfath Beigi, Kamran Divaani-Aazar, Massoud Tousi (2022)

Czechoslovak Mathematical Journal

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Let $R$ be a local ring and $C$ a semidualizing module of $R$ . We investigate the behavior of certain classes of generalized Cohen-Macaulay $R$ -modules under the Foxby equivalence between the Auslander and Bass classes with respect to $C$ . In particular, we show that generalized Cohen-Macaulay $R$ -modules are invariant under this equivalence and if $M$ is a finitely generated $R$ -module in the Auslander class with respect to $C$ such that $C \otimes_{R} M$ is surjective Buchsbaum, then $M$ is also surjective Buchsbaum. ...

Dual modules and reflexive modules with respect to a semidualizing module

Lixin Mao (2024)

Czechoslovak Mathematical Journal

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Let $C$ be a semidualizing module over a commutative ring. We first investigate the properties of $C$ -dual, $C$ -torsionless and $C$ -reflexive modules. Then we characterize some rings such as coherent rings, $Π$ -coherent rings and FP-injectivity of $C$ using $C$ -dual, $C$ -torsionless and $C$ -reflexive properties of some special modules.

On $n$ -submodules and $G . n$ -submodules

Somayeh Karimzadeh, Javad Moghaderi (2023)

Czechoslovak Mathematical Journal

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We investigate some properties of $n$ -submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an $n$ -submodule. Also, we show that if $M$ is a finitely generated $R$ -module and $\sqrt{{Ann}_{R} (M)}$ is a prime ideal of $R$ , then $M$ has $n$ -submodule. Moreover, we define the notion of $G . n$ -submodule, which is a generalization of the notion of $n$ -submodule. We find some characterizations of $G . n$ -submodules and we examine the way the aforementioned notions are related...

Finitistic dimension and restricted injective dimension

Dejun Wu (2015)

Czechoslovak Mathematical Journal

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We study the relations between finitistic dimensions and restricted injective dimensions. Let $R$ be a ring and $T$ a left $R$ -module with $A = {End}_{R} T$ . If $_{R} T$ is selforthogonal, then we show that $rid (T_{A}) \leq findim (A_{A}) \leq findim (_{R} T) + rid (T_{A})$ . Moreover, if $R$ is a left noetherian ring and $T$ is a finitely generated left $R$ -module with finite injective dimension, then $rid (T_{A}) \leq findim (A_{A}) \leq fin . inj . \dim (_{R} R) + rid (T_{A})$ . Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension.

Special modules for $R (PSL (2, q))$

Liufeng Cao, Huixiang Chen (2023)

Czechoslovak Mathematical Journal

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Let $R$ be a fusion ring and $R_{ℂ} : = R \otimes_{ℤ} ℂ$ be the corresponding fusion algebra. We first show that the algebra $R_{ℂ}$ has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, $R_{ℂ}$ admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra $R (PSL (2, q)) : = r (PSL (2, q)) \otimes_{ℤ} ℂ$ up to isomorphism, where $r (PSL (2, q))$ is the...

On the convergence and character spectra of compact spaces

István Juhász, William A. R. Weiss (2010)

Fundamenta Mathematicae

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An infinite set A in a space X converges to a point p (denoted by A → p) if for every neighbourhood U of p we have |A∖U| < |A|. We call cS(p,X) = |A|: A ⊂ X and A → p the convergence spectrum of p in X and cS(X) = ⋃cS(x,X): x ∈ X the convergence spectrum of X. The character spectrum of a point p ∈ X is χS(p,X) = χ(p,Y): p is non-isolated in Y ⊂ X, and χS(X) = ⋃χS(x,X): x ∈ X is the character spectrum of X. If κ ∈ χS(p,X) for a compactum X then κ,cf(κ) ⊂ cS(p,X). A selection of our...

Some results on $G_{C}$ -flat dimension of modules

Ramalingam Udhayakumar, Intan Muchtadi-Alamsyah, Chelliah Selvaraj (2019)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study some properties of $G_{C}$ -flat $R$ -modules, where $C$ is a semidualizing module over a commutative ring $R$ and we investigate the relation between the $G_{C}$ -yoke with the $C$ -yoke of a module as well as the relation between the $G_{C}$ -flat resolution and the flat resolution of a module over $G F$ -closed rings. We also obtain a criterion for computing the $G_{C}$ -flat dimension of modules.

A spectral mapping theorem for Banach modules

H. Seferoğlu (2003)

Studia Mathematica

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Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then $σ (T_{μ}) = \bar{μ ̂ (s p (X))}$ for each measure μ in reg(M(G)), where $T_{μ}$ denotes the operator in B(X) defined by $T_{μ} x = μ \circ x$ , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal $I_{X} = f \in L ¹ (G) | T_{f} = 0$ , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains...

Generalized tilting modules over ring extension

Zhen Zhang (2019)

Czechoslovak Mathematical Journal

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Let $Γ$ be a ring extension of $R$ . We show the left $Γ$ -module $U = Γ \otimes_{R} C$ with the endmorphism ring End $_{Γ} U = Δ$ is a generalized tilting module when $_{R} C$ is a generalized tilting module under some conditions.

On linear extension for interpolating sequences

Eric Amar (2008)

Studia Mathematica

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Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces $H^{p} (σ)$ and the $H^{p} (σ)$ interpolating sequences S in the p-spectrum $ℳ_{p}$ of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is $H^{s} (σ)$ -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in $H^{\infty} ()$ then S is $H^{p} ()$ -interpolating with...