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

Similarity:

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

Tsiu-Kwen Lee, Yiqiang Zhou (2008)

Colloquium Mathematicae

Similarity:

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

Similarity:

Note on strongly nil clean elements in rings

Aleksandra Kostić, Zoran Z. Petrović, Zoran S. Pucanović, Maja Roslavcev (2019)

Czechoslovak Mathematical Journal

Similarity:

Let $R$ be an associative unital ring and let $a \in R$ be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these...

Vortex rings for the Gross-Pitaevskii equation

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

Journal of the European Mathematical Society

Similarity:

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

Similarity:

Rings with divisibility on descending chains of ideals

Oussama Aymane Es Safi, Najib Mahdou, Ünsal Tekir (2024)

Czechoslovak Mathematical Journal

Similarity:

This paper deals with the rings which satisfy $D C C_{d}$ condition. This notion has been introduced recently by R. Dastanpour and A. Ghorbani (2017) as a generalization of Artnian rings. It is of interest to investigate more deeply this class of rings. This study focuses on commutative case. In this vein, we present this work in which we examine the transfer of these rings to the trivial, amalgamation and polynomial ring extensions. We also investigate the relationship between this class of rings...

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

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

Colloquium Mathematicae

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

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...

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

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