Mal'tsev--Neumann products of semi-simple classes of rings

Barry James Gardner

Displaying similar documents to “Mal'tsev--Neumann products of semi-simple classes of rings”

Property of being semi-Kelley for the cartesian products and hyperspaces

Enrique Castañeda-Alvarado, Ivon Vidal-Escobar (2017)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we construct a Kelley continuum $X$ such that $X \times [0, 1]$ is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. In addition, we show that the hyperspace $C (X)$ is not semi- Kelley. Further we show that small Whitney levels in $C (X)$ are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro,...

Some generalisations of $T_{D}$ spaces

S. P. Arya, M. P. Bhamini (1982)

Matematički Vesnik

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On pairwise semi $R_{0}$ and pairwise semi $R_{1}$ bitopological spaces

M. Jelić (1982)

Matematički Vesnik

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On $(n, m)$ - $A$ -normal and $(n, m)$ - $A$ -quasinormal semi-Hilbertian space operators

Samir Al Mohammady, Sid Ahmed Ould Beinane, Sid Ahmed Ould Ahmed Mahmoud (2022)

Mathematica Bohemica

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The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let $ℋ$ be a Hilbert space and let $A$ be a positive bounded operator on $ℋ$ . The semi-inner product ${〈 h ∣ k 〉}_{A} : = 〈 A h ∣ k 〉$ , $h, k \in ℋ$ , induces a semi-norm ${∥ \cdot ∥}_{A}$ . This makes $ℋ$ into a semi-Hilbertian space. An operator $T \in ℬ_{A} (ℋ)$ is said to be $(n, m)$ - $A$ -normal if $[T^{n}, {(T^{♯_{A}})}^{m}] : = T^{n} {(T^{♯_{A}})}^{m} - {(T^{♯_{A}})}^{m} T^{n} = 0$ for some positive integers $n$ and $m$ .

Some properties of the topology of $α$ -sets

D. Andrijević (1984)

Matematički Vesnik

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Some results on semi-total signed graphs

Deepa Sinha, Pravin Garg (2011)

Discussiones Mathematicae Graph Theory

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A signed graph (or sigraph in short) is an ordered pair $S = (S^{u}, σ)$ , where $S^{u}$ is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of $S^{u}$ into the set +,-, called the signature of S. The ×-line sigraph of S denoted by $L_{\times} (S)$ is a sigraph defined on the line graph $L (S^{u})$ of the graph $S^{u}$ by assigning to each edge ef of $L (S^{u})$ , the product of signs of the adjacent edges e and f in S. In this paper, first we define semi-total line sigraph and semi-total point sigraph...

Some results on semi-stratifiable spaces

Wei-Feng Xuan, Yan-Kui Song (2019)

Mathematica Bohemica

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We study relationships between separability with other properties in semi-stratifiable spaces. Especially, we prove the following statements: (1) If $X$ is a semi-stratifiable space, then $X$ is separable if and only if $X$ is $D C (ω_{1})$ ; (2) If $X$ is a star countable extent semi-stratifiable space and has a dense metrizable subspace, then $X$ is separable; (3) Let $X$ be a $ω$ -monolithic star countable extent semi-stratifiable space. If $t (X) = ω$ and $d (X) \leq ω_{1}$ , then $X$ is hereditarily separable. Finally, we prove that for...

Migrativity properties of 2-uninorms over semi-t-operators

Ying Li-Jun, Qin Feng (2022)

Kybernetika

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In this paper, we analyze and characterize all solutions about $α$ -migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$ , $C_{k}^{0}$ , $C_{k}^{1}$ , $C_{1}^{0}$ , $C_{0}^{1}$ , over semi-t-operators. We give the sufficient and necessary conditions that make these $α$ -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G \in C^{k}$ , the $α$ -migrativity of $G$ over a semi-t-operator $F_{μ, ν}$ is closely related to the $α$ -section of $F_{μ, ν}$ or the ordinal sum representation...

Multiple solutions to a perturbed Neumann problem

Giuseppe Cordaro (2007)

Studia Mathematica

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We consider the perturbed Neumann problem ⎧ -Δu + α(x)u = α(x)f(u) + λg(x,u) a.e. in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where Ω is an open bounded set in $ℝ^{N}$ with boundary of class C², $α \in L^{\infty} (Ω)$ with $e s s i n f_{Ω} α > 0$ , f: ℝ → ℝ is a continuous function and g: Ω × ℝ → ℝ, besides being a Carathéodory function, is such that, for some p > N, $s u p_{| s | \leq t} | g (\cdot, s) | \in L^{p} (Ω)$ and $g (\cdot, t) \in L^{\infty} (Ω)$ for all t ∈ ℝ. In this setting, supposing only that the set of global minima of the function $1 / 2 ξ ² - \int_{0}^{ξ} f (t) d t$ has M ≥ 2 bounded connected components, we prove that, for all λ ∈ ℝ small enough,...

Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

Giovanni Anello, Giuseppe Cordaro (2003)

Colloquium Mathematicae

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We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ $- Δ_{p} u + λ (x) {| u |}^{p - 2} u = μ f (x, u)$ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ \in L^{\infty} (Ω)$ with $e s s i n f_{x \in Ω} λ (x) > 0$ and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.

A subclass of strongly clean rings

Orhan Gurgun, Sait Halicioglu and Burcu Ungor (2015)

Communications in Mathematics

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In this paper, we introduce a subclass of strongly clean rings. Let $R$ be a ring with identity, $J$ be the Jacobson radical of $R$ , and let $J^{#}$ denote the set of all elements of $R$ which are nilpotent in $R / J$ . An element $a \in R$ is called provided that there exists an idempotent $e \in R$ such that $a e = e a$ and $a - e$ or $a + e$ is an element of $J^{#}$ . A ring $R$ is said to be in case every element in $R$ is very $J^{#}$ -clean. We prove that every very $J^{#}$ -clean ring is strongly $π$ -rad clean and has stable range one. It is shown that for a...

The number of conjugacy classes of elements of the Cremona group of some given finite order

Jérémy Blanc (2007)

Bulletin de la Société Mathématique de France

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This note presents the study of the conjugacy classes of elements of some given finite order $n$ in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if $n$ is even, $n = 3$ or $n = 5$ , and that it is equal to $3$ (respectively $9$ ) if $n = 9$ (respectively if $n = 15$ ) and to $1$ for all remaining odd orders. Some precise representative elements of the classes are given.

On a Kleinecke-Shirokov theorem

Vasile Lauric (2021)

Czechoslovak Mathematical Journal

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We prove that for normal operators $N_{1}, N_{2} \in ℒ (ℋ),$ the generalized commutator $[N_{1}, N_{2}; X]$ approaches zero when $[N_{1}, N_{2}; [N_{1}, N_{2}; X]]$ tends to zero in the norm of the Schatten-von Neumann class $𝒞_{p}$ with $p > 1$ and $X$ varies in a bounded set of such a class.

Products of conjugacy classes in finite unitary groups $G U (3, q^{2})$ and $S U (3, q^{2})$

S.Yu. Orevkov (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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For the groups $G U (3)$ , $S U (3)$ , $G L (3)$ , $S U (3)$ over a finite field we solve the class product problem, i.e., we give a complete list of $m$ -tuples of conjugacy classes whose product does not contain the identity matrix.