Almost Prüfer v-multiplication domains and the ring $D + XD_S[X]$

Qing Li

Displaying similar documents to “Almost Prüfer v-multiplication domains and the ring $D + X D_{S} [X]$ ”

Special sets of reals and weak forms of normality on Isbell--Mrówka spaces

Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki (2023)

Commentationes Mathematicae Universitatis Carolinae

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We recall some classical results relating normality and some natural weakenings of normality in $Ψ$ -spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$ -sets, $λ$ -sets and $σ$ -sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being $ℵ_{0}$ -separated. This new class fits between $λ$ -sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $𝒜$ being...

Asymmetric tie-points and almost clopen subsets of $ℕ^{*}$

Alan S. Dow, Saharon Shelah (2018)

Commentationes Mathematicae Universitatis Carolinae

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A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of $ℕ^{*}$ . One especially important application, due to Veličković, was to the existence of nontrivial involutions on $ℕ^{*}$ . A tie-point of $ℕ^{*}$ has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost...

(Generalized) filter properties of the amalgamated algebra

Yusof Azimi (2022)

Archivum Mathematicum

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Let $R$ and $S$ be commutative rings with unity, $f : R \to S$ a ring homomorphism and $J$ an ideal of $S$ . Then the subring $R ⋈^{f} J : = {(a, f (a) + j) ∣ a \in R$ and $j \in J}$ of $R \times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$ . In this paper, we determine when $R ⋈^{f} J$ is a (generalized) filter ring.

On Bhargava rings

Mohamed Mahmoud Chems-Eddin, Omar Ouzzaouit, Ali Tamoussit (2023)

Mathematica Bohemica

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Let $D$ be an integral domain with the quotient field $K$ , $X$ an indeterminate over $K$ and $x$ an element of $D$ . The Bhargava ring over $D$ at $x$ is defined to be $𝔹_{x} (D) : = {f \in K [X] : for all a \in D, f (x X + a) \in D [X]}$ . In fact, $𝔹_{x} (D)$ is a subring of the ring of integer-valued polynomials over $D$ . In this paper, we aim to investigate the behavior of $𝔹_{x} (D)$ under localization. In particular, we prove that $𝔹_{x} (D)$ behaves well under localization at prime ideals of $D$ , when $D$ is a locally finite intersection of localizations. We also attempt a classification of integral...

Maximal non-pseudovaluation subrings of an integral domain

Rahul Kumar (2024)

Czechoslovak Mathematical Journal

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The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R \subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$ , and for any ring $T$ such that $R \subset T \subset S$ , $T$ is a pseudovaluation subring of $S$ . We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$ . We also characterize maximal non-pseudovaluation subrings of a local integral domain.

A note on Skolem-Noether algebras

Juncheol Han, Tsiu-Kwen Lee, Sangwon Park (2021)

Czechoslovak Mathematical Journal

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The paper was motivated by Kovacs’ paper (1973), Isaacs’ paper (1980) and a recent paper, due to Brešar et al. (2018), concerning Skolem-Noether algebras. Let $K$ be a unital commutative ring, not necessarily a field. Given a unital $K$ -algebra $S$ , where $K$ is contained in the center of $S$ , $n \in ℕ$ , the goal of this paper is to study the question: when can a homomorphism $φ : M_{n} (K) \to M_{n} (S)$ be extended to an inner automorphism of $M_{n} (S)$ ? As an application of main results presented in the paper, it is proved that if $S$ is...

P-injective group rings

Liang Shen (2020)

Czechoslovak Mathematical Journal

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A ring $R$ is called right P-injective if every homomorphism from a principal right ideal of $R$ to $R_{R}$ can be extended to a homomorphism from $R_{R}$ to $R_{R}$ . Let $R$ be a ring and $G$ a group. Based on a result of Nicholson and Yousif, we prove that the group ring $RG$ is right P-injective if and only if (a) $R$ is right P-injective; (b) $G$ is locally finite; and (c) for any finite subgroup $H$ of $G$ and any principal right ideal $I$ of $RH$ , if $f \in {Hom}_{R} (I_{R}, R_{R})$ , then there exists $g \in {Hom}_{R} ({RH}_{R}, R_{R})$ such that ${g |}_{I} = f$ . Similarly, we also obtain equivalent...

Connectedness of some rings of quotients of $C (X)$ with the $m$ -topology

F. Azarpanah, M. Paimann, A. R. Salehi (2015)

Commentationes Mathematicae Universitatis Carolinae

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In this article we define the $m$ -topology on some rings of quotients of $C (X)$ . Using this, we equip the classical ring of quotients $q (X)$ of $C (X)$ with the $m$ -topology and we show that $C (X)$ with the $r$ -topology is in fact a subspace of $q (X)$ with the $m$ -topology. Characterization of the components of rings of quotients of $C (X)$ is given and using this, it turns out that $q (X)$ with the $m$ -topology is connected if and only if $X$ is a pseudocompact almost $P$ -space, if and only if $C (X)$ with $r$ -topology is connected. We also...

Pluriharmonic extension in proper image domains

Rafał Czyż (2009)

Annales Polonici Mathematici

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Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s ≥ 3. Also let $Ω_{π}$ be the image of D under the proper holomorphic map π. We characterize those continuous functions $f : \partial Ω_{π} \to ℝ$ that can be extended to a real-valued pluriharmonic function in $Ω_{π}$ .

The clean elements of the ring $ℛ (L)$

Ali Akbar Estaji, Maryam Taha (2024)

Czechoslovak Mathematical Journal

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We characterize clean elements of $ℛ (L)$ and show that $α \in ℛ (L)$ is clean if and only if there exists a clopen sublocale $U$ in $L$ such that $𝔠_{L} (coz (α - 1)) \subseteq U \subseteq 𝔬_{L} (coz (α))$ . Also, we prove that $ℛ (L)$ is clean if and only if $ℛ (L)$ has a clean prime ideal. Then, according to the results about $ℛ (L),$ we immediately get results about $𝒞_{c} (L) .$

Strongly 2-nil-clean rings with involutions

Huanyin Chen, Marjan Sheibani Abdolyousefi (2019)

Czechoslovak Mathematical Journal

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A $*$ -ring $R$ is strongly 2-nil- $*$ -clean if every element in $R$ is the sum of two projections and a nilpotent that commute. Fundamental properties of such $*$ -rings are obtained. We prove that a $*$ -ring $R$ is strongly 2-nil- $*$ -clean if and only if for all $a \in R$ , $a^{2} \in R$ is strongly nil- $*$ -clean, if and only if for any $a \in R$ there exists a $*$ -tripotent $e \in R$ such that $a - e \in R$ is nilpotent and $e a = a e$ , if and only if $R$ is a strongly $*$ -clean SN ring, if and only if $R$ is abelian, $J (R)$ is nil and $R / J (R)$ is $*$ -tripotent. Furthermore, we explore...

A remark on separate holomorphy

Marek Jarnicki, Peter Pflug (2006)

Studia Mathematica

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Let X be a Riemann domain over $ℂ^{k} \times ℂ^{ℓ}$ . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set $P \subset ℂ^{k}$ such that every slice $X_{a}$ of X with a∉ P is a region of holomorphy with respect to the family ${f |}_{X_{a}} : f \in ℱ$ .

Displaying similar documents to “Almost Prüfer v-multiplication domains and the ring D + X D S [ X ] ”

Displaying similar documents to “Almost Prüfer v-multiplication domains and the ring $D + X D_{S} [X]$ ”