Skeletons, bodies and generalized $E(R)$-algebras

Rüdiger Göbel; Daniel Herden; Saharon Shelah

Displaying similar documents to “Skeletons, bodies and generalized $E (R)$ -algebras”

Rings of $(γ, δ)$ type

Kleinfeld, Erwin (1959)

Portugaliae mathematica

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A unified approach to the Armendariz property of polynomial rings and power series rings

Tsiu-Kwen Lee, Yiqiang Zhou (2008)

Colloquium Mathematicae

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A ring R is called Armendariz (resp., Armendariz of power series type) if, whenever $(\sum_{i \geq 0} a_{i} x^{i}) (\sum_{j \geq 0} b_{j} x^{j}) = 0$ in R[x] (resp., in R[[x]]), then $a_{i} b_{j} = 0$ for all i and j. This paper deals with a unified generalization of the two concepts (see Definition 2). Some known results on Armendariz rings are extended to this more general situation and new results are obtained as consequences. For instance, it is proved that a ring R is Armendariz of power series type iff the same is true of R[[x]]. For an injective endomorphism...

О регулярных самоинъективных и о $V$ -кольцах

Д.В. Тюкавкин, D. V. Tjukavkin, D. V. Tǔkavkin, D. V. Tjukavkin (1994)

Algebra i Logika

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Vortex rings for the Gross-Pitaevskii equation

Fabrice Bethuel, G. Orlandi, Didier Smets (2004)

Journal of the European Mathematical Society

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We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension $N \geq 3$ . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if $N = 3$ ).

О наследственности радикалов колец типа $(γ *)$ .

А.С. Марковичев (1978)

Algebra i Logika

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An intermediate ring between a polynomial ring and a power series ring

M. Tamer Koşan, Tsiu-Kwen Lee, Yiqiang Zhou (2013)

Colloquium Mathematicae

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Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]: [R;I][x]: = $\sum_{i \geq 0} r_{i} x^{i} \in R [[x]]$ : ∃ 0 ≤ n∈ ℤ such that $r_{i} \in I$ , ∀ i ≥ n. The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with...

On modules and rings with the restricted minimum condition

M. Tamer Koşan, Jan Žemlička (2015)

Colloquium Mathematicae

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A module M satisfies the restricted minimum condition if M/N is artinian for every essential submodule N of M. A ring R is called a right RM-ring whenever $R_{R}$ satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring R is proved to be an RM-ring if and only if R/Soc(R) is noetherian and every singular module is semiartinian.

Moduled categories and adjusted modules over traced rings

Daniel Simson

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CONTENTS1. Introduction.......................................................................................52. Traced rings and adjusted modules..................................................93. Moduled categories.........................................................................214. Triangular adjustments....................................................................325. Categories of matrices and $_{A} M_{B}$ -matrix modules...............436. Trace and cotrace reductions.........................................................477....

Sagbi bases of Cox–Nagata rings

Bernd Sturmfels, Zhiqiang Xu (2010)

Journal of the European Mathematical Society

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We degenerate Cox–Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev–Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective $n$ -space at $n + 3$ points, sagbi bases of Cox–Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D’Cruz–Iarrobino...

A commutativity theorem for associative rings

Mohammad Ashraf (1995)

Archivum Mathematicum

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Let $m > 1, s \geq 1$ be fixed positive integers, and let $R$ be a ring with unity $1$ in which for every $x$ in $R$ there exist integers $p = p (x) \geq 0, q = q (x) \geq 0, n = n (x) \geq 0, r = r (x) \geq 0$ such that either $x^{p} [x^{n}, y] x^{q} = x^{r} [x, y^{m}] y^{s}$ or $x^{p} [x^{n}, y] x^{q} = y^{s} [x, y^{m}] x^{r}$ for all $y \in R$ . In the present paper it is shown that $R$ is commutative if it satisfies the property $Q (m)$ (i.e. for all $x, y \in R, m [x, y] = 0$ implies $[x, y] = 0$ ).

Cartan-Eilenberg projective, injective and flat complexes

Xiaorui Zhai, Chunxia Zhang (2016)

Czechoslovak Mathematical Journal

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Let $R$ be an associative ring with identity and $ℱ$ a class of $R$ -modules. In this article: we first give a detailed treatment of Cartan-Eilenberg $ℱ$ complexes and extend the basic properties of the class $ℱ$ to the class $CE (ℱ$ ). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these...

Generalized E-algebras via λ-calculus I

Rüdiger Göbel, Saharon Shelah (2006)

Fundamenta Mathematicae

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An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra $E n d_{R} A$ of the R-module $_{R} A$ , taking any a ∈ A to the right multiplication $a_{r} \in E n d_{R} A$ by a, is an isomorphism of algebras. In this case $_{R} A$ is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18,...

On $K$ -Boolean Rings

W. B. Vasantha Kandasamy (1992)

Publications du Département de mathématiques (Lyon)

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A Characterization of One-Element p-Bases of Rings of Constants

Piotr Jędrzejewicz (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in $K [x ₁^{p}, . . ., x ₙ^{p}]$ . We prove that $K [x ₁^{p}, . . ., x ₙ^{p}, f]$ is the ring of constants of a K-derivation of K[x₁,...,xₙ] if and only if all the partial derivatives of f are relatively prime. The proof is based on a generalization of Freudenburg’s lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.

Bounds for quotients in rings of formal power series with growth constraints

Vincent Thilliez (2002)

Studia Mathematica

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In rings $Γ_{M}$ of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence $M = {(M_{l})}_{l \geq 0}$ (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in $Γ_{M}$ such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to $Γ_{M}$ , provided $Γ_{M}$ is stable under derivation. By a further development of the method, we obtain the main result of the paper,...

Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions

Adrien Deloro (2013)

Confluentes Mathematici

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We classify quadratic ${SL}_{2} (𝕂)$ - and ${𝔰𝔩}_{2} (𝕂)$ -modules by crude computation, generalising in the first case a Theorem proved independently by F.G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearisation results for abstract modules of algebraic groups and associated Lie rings.

Displaying similar documents to “Skeletons, bodies and generalized E ( R ) -algebras”

Displaying similar documents to “Skeletons, bodies and generalized $E (R)$ -algebras”