Semidistributive Laurent Series Rings

非结合斜洛朗多项式环的简单性

Simplicity of non-associative skew Laurent polynomial rings

本文引入非结合斜洛朗多项式环，刻画了其简单性的条件，并推广了 Jordan、Voskoglou、Nystedt 和 Öinert 的相关结果。

$\aleph_0$-distributive modules and rings

Let $A$ be a ring with minimum condition on principal right ideals. It is proved that $\aleph_0$-distributive right (left) $A$-modules coincide with Artinian (Noetherian) right (left) $A$-modules. Rings, over which all right modules are direct sums of $\aleph_0$-distributive coincide with rings of of finite representation type. Rings, whose right modules are semidistributive, coincide with Kawada rings, over basis rings of which all right modules are completely cyclic. The studies of Tuganbaev are supported by Russian Scientific Foundation, project 22-11-00052.

斜洛朗级数除环中的换位子乘积

Commutator products in skew Laurent series division rings

针对非交换除环元素能否表示为两个换位子乘积的问题，本文对域上的斜洛朗级数除环给出了肯定答案，推进了单环与除环结构相关研究。

Goldie twisted partial skew power series rings

In this article, we work with unital twisted partial action of $\mathbb{Z}$ on an unital ring $R$ and we introduce the twisted partial skew power series rings and twisted partial skew Laurent series rings. We study primality, semi-primality and prime ideals in these rings. We completely describe the prime radical in partial skew Laurent series rings. Moreover, we study the Goldie property in partial skew power series rings and partial skew Laurent series rings and we describe conditions of the semiprimality of twisted partial skew power series rings.

斜洛朗级数环在戴德金整环上的研究

Skew Laurent Series Ring Over a Dedekind Domain

本文证明交换戴德金整环上的斜洛朗级数环是非交换戴德金整环，并在自同构平凡作用于理想类群时给出其K_0群同构及维数、秩等不变量。

$ω$-Euclidean domain and skew Laurent series rings

In this paper we proved that if $R$ is right $ω$-Euclidean domain, then skew Laurent formal series ring is right $ω$-Euclidean domain. We also showed that if $R$ is a right $ω$-Euclidean domain with multiplicative norm, then skew Laurent formal series ring is a right principal ideal domain. In addition, we proved that if $R$ is a noncommutative $ω$-Euclidean domain with a multiplicative norm, then $R$ and skew Laurent formal series ring is a ring with elementary reduction of matrices.

非结合系数环上的非结合斜幂级数环与非结合斜洛朗级数环的希尔伯特基定理

The Hilbert Basis Theorem for Non-Associative Skew Power Series Rings and Non-Associative Skew Laurent Series Rings over a Non-Associative Coefficient Ring

本文为非结合斜幂级数环和斜洛朗级数环建立希尔伯特基定理，通过引入拟结合性质给出Noetherian条件，并指出一般非结合情形下定理不成立。

可逆斜Laurent多项式环与Poisson自同构的变形

Reversible skew Laurent polynomial rings and deformations of Poisson automorphisms

一个斜Laurent多项式环R[x^{ \pm 1};α]是可逆的，如果它有一个可逆的自同构，也就是说，一个周期为2的自同构，它转置x和x^{-1}并限制于R的一个自同构。我们研究了可逆自同构的不变量，并应用我们的方法确定了两个简单斜Laurent多项式环的可逆自同构的不变量环，即二维非交换可解李代数的包络代数和量子环面的坐标环的局部化.这两个斜Laurent多项式环是Poisson代数的变形，我们将它们的逆自同构和不变量解释为Poisson自同构和不变量的变形.

非交叉积的扭曲洛朗级数环

A twisted Laurent series ring that is a noncrossed product

关于非交叉积的惊人结果是它们的存在（Amitsur）和Q（t）和Q（（t））作为它们的最小可能中心（Risksel）的确定。本文给出了Q（（t））上的第一个完全显式非交叉积的例子.因此，使用深数论定理（局部-全局原理，如Hasse范数定理和密度定理）来证明存在性被消除了。相反，该示例可以通过直接计算来验证。非交叉积的证明是简单而简短的。

斜Laurent级数与一般循环卷积码

Skew Laurent Series and General Cyclic Convolutional Codes

本文研究了斜Laurent级数在构造一般循环卷积码中的作用，并探讨了如何处理斜导出带来的困难。

Continuous homomorphisms between algebras of iterated Laurent series over a ring

We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we give a criterion of invertibility of an endomorphism and provide an explicit formula for the inverse endomorphism. We study the behavior of the higher-dimensional residue under continuous homomorphisms.

The ascending chain condition for principal left or right ideals of skew generalized power series rings

Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $ω: S\rightarrow End(R)$ a monoid homomorphism. In this paper we study the ascending chain conditions on principal left (resp. right) ideals of the skew generalized power series ring $R[[S,ω]]$. Among other results, it is shown that $R[[S,ω]]$ is a right archimedean reduced ring if $S$ is an Artinian strictly totally ordered monoid, $R$ is a right archimedean and $S$-rigid ring which satisfies the ACC on annihilators and $ω_s$ preserves nonunits of $R$ for each $s\in S$. As a consequence we deduce that the power series rings, Laurent …

素特征Laurent多项式代数上微分算子环的保序自同构群

The group of order preserving automorphisms of the ring of differential operators on Laurent polynomial algebra in prime characteristic

令$K$是特征$p>0$的域。证明了Laurent多项式代数$L_n:= K[x_1^{\pm 1}, ..., x_n^{\pm 1}]$上的微分算子环$\CD (L_n)$的保序自同构群$\Aut_{ord}(\CD (L_n))$同构于群$\Zp^n \rtimes \Aut_K(L_n)$的斜直积，其中$\Zp$是$p$进整数环.此外，还明确地找到了群$\Aut_{ord}(\CD (L_n))$。类似地，$\Aut_{ord}(\CDPn)\simeq \Aut_K(P_n)$，其中$P_n: =K[x_1, ..., x_n]$是多项式代数。

On $q$-commutative power and Laurent series rings at roots of unity

We continue the first and second authors' study of $q$-commutative power series rings $R=k_q[[x_1,\ldots,x_n]]$ and Laurent series rings $L=k_q[[x^{\pm 1}_1,\ldots,x^{\pm 1}_n]]$, specializing to the case in which the commutation parameters $q_{ij}$ are all roots of unity. In this setting, $R$ is a PI algebra, and we can apply results of De Concini, Kac, and Procesi to show that $L$ is an Azumaya algebra whose degree can be inferred from the $q_{ij}$. Our main result establishes an exact criterion (dependent on the $q_{ij}$) for determining when the centers of $L$ and $R$ are commutative Laure…

希尔伯特基定理的非结合版本

Non-associative versions of Hilbert's basis theorem

该研究针对四类非结合代数结构证明了新版本的希尔伯特基定理，明确了非结合Ore扩张与斜洛朗多项式环的基定理左右版本成立性差异，补充了结合代数中不存在的结论。

拟双斜多项式环

Quasi-Duo Skew Polynomial Rings

给出了右（左）拟duo自同态型斜多项式环和斜Laurent多项式环的一个刻划.特别地，证明了（1）多项式环R[x]是右拟duo当且仅当R[x]是交换模其Jacobson根当且仅当R[x]是左拟duo;（2）斜Laurent多项式环是右拟duo当且仅当它是左拟duo.这些结果推广了关于拟duo多项式环的一个刻画的一些已知结果，并部分回答了Lam和Dugas提出的右拟duo环是否是左拟duo环的问题.

Pseudo-Sylvester domains and skew Laurent polynomials over firs

Building on recent work of Jaikin-Zapirain, we provide a homological criterion for a ring to be a pseudo-Sylvester domain, that is, to admit a division ring of fractions over which all stably full matrices become invertible. We use the criterion to study skew Laurent polynomial rings over free ideal rings (firs). As an application of our methods, we prove that crossed products of division rings with free-by-{infinite cyclic} and surface groups are pseudo-Sylvester domains unconditionally and Sylvester domains if and only if they admit stably free cancellation. This relies on the recent proof o…

Laurent对称函数

Laurent Symmetric Functions

本文用生成元和关系刻画Laurent对称多项式环，推广Hall内积并证明Laurent Schur多项式构成标准正交基，在无穷变量情形将其实现为逆向极限的直接极限，并关联到一般线性群表示的特征。

斜广义幂级数的左App环

Left-App rings of skew generalized power series

如果左零化子$l_{R}(Ra)$是右$s$ -单位元，作为任何$a\in R$的$R$的理想，则环$R$称为左APP-环。设$R$是环，$(S,\leq)$是严格序幺半群，$ω:S\longrightarrow {\rm End}(R)$是幺半群同态.斜广义幂级数环$[[R^{S,\leq},ω]]$是（斜）多项式环、（斜）幂级数环、（斜）Laurent多项式环、（斜）群环和Malcev-Neumann Laurent级数环的一个普通推广。研究了斜广义幂级数环$[[R^{S,\leq},ω]]$的左APP-性质。证明了：若$(S,\leq)$是严格全序幺半群，$ω:S\longrightarrow {\rm Aut}(R)$是幺半群同态，$R$是右零化子满足降链条件的环，则$[[R^{S,\leq},ω]]$是左APP当且仅当对$R$的任意$S$ -指标子集$A$，理想$l_{R}\big(\sum_{a\in A}\sum_{s\in S}Rω_{s}(a)\big)$是右$s$ -酉的.

关于Stafford的一个定理

On a theorem of Stafford

Stafford证明了Weyl代数A_n（K）的每个左理想或右理想都由两个元素生成.本文证明了形式洛朗级数域K（（x_1，.）上的微分算子环的每一个左理想或右理想x_n））也由两个元素生成。对于收敛的洛朗级数C{x_1，.，x_n}。这与一个猜想是一致的，即在一个（非交换的）诺特单环中，每个左理想或右理想都是由两个元素生成的。

广义幂级数环上的Rota-Baxter算子

Rota-Baxter operators on generalized power series rings

Rota-Baxter代数在量子场论应用中的一个重要例子是具有适当投影的洛朗级数环。我们把洛朗级数环看作指数在有序幺半群上的广义幂级数环的一个特例。我们研究了广义幂级数环何时有Rota-Baxter算子，以及它与有序幺半群的关系。

S-Noetherian generalized power series rings

Let R be a ring with identity, (M;\leq) a commutative positive strictly ordered monoid and w_m an automorphism for each m \in M . The skew generalized power series ring R[[M,w]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev Neumann Laurent series rings. If S\subset R is a multiplicative set, then R is called right S-Noetherian, if for each ideal I of R, Is \subseteq J\subseteq I for some s\in S and some finitely generated right ideal J . Unifying and generalizing a number of known results, we s…

cP-Baer环的多项式扩张

Polynomial extensions of cP-Baer rings

本文研究cP-Baer性质在斜多项式、斜Laurent多项式、斜幂级数、斜逆Laurent级数及幺半群环等各类环扩张中的传递规律，并回答了Birkenmeier与Heider提出的一个问题。

斜幂级数环的局部化与完备化

Localisations and Completions of Skew Power Series Rings

本文是[P. Schneider和O. Venjakob，On the codimension of modules over skew幂级数环及其在岩泽代数上的应用，J. Pure Appl. Algebra 204（2005），349 - 367.].构造了斜洛朗级数环B，并证明了斜幂级数环A的某些典型Ore集S的存在性，使得局部化A_S的某个完备化与B同构.这是适用于某些岩泽代数。最后引入了过收敛斜洛朗级数环的子环。

Malcev-Neumann级数环中的自由域

Free fields in Malcev-Neumann series rings

证明了序群的Malcev-Neumann级数的除环中经常包含一个可数秩自由域，即可数秩自由结合代数的分式泛域.这是自由域在除环上的可嵌入性准则的一个应用，这些域是关于K的赋值函数完备的。千叶本文还讨论了斜洛朗级数环的其它应用。最后，还讨论了Malcev-Neumann级数环中不可数秩自由域的可嵌入性问题。

$\mathbb{F}_p((X))$ is decidable as a module over the ring of additive polynomials

Let $p$ be a prime number, $K$ be the henselization of the rational functions over the finite field $\mathbb{F}_p$ and $R$ be the ring of additive polynomials over K. We show that the field of Laurent series over $\mathbb{F}_p$ is decidable seen as an R-module. Moreover, we provide a recursively enumerable axiom system (satisfied by $K$) in the language of $R$-modules together with a unary predicate for the valuation ring, modulo which every positive primitive formula is equivalent to a universal formula. Consequently the $R$-module theory of the field of Laurent series is model-complete in th…

与强Z分级环相关的射影线的代数K-理论

The algebraic $K$-theory of the projective line associated with a strongly $\mathbb{Z}$-graded ring

本文研究了强Z分级环与射影线的代数K-理论，探讨了K-理论的分解性质及其在一般强Z分级环中的推广。

具有 McCoy 性质的斜广义幂级数环

Skew Generalized Power Series Rings With the McCoy Property

本文研究了斜广义幂级数环上的 $(S,ω)$-McCoy 条件，将标准 McCoy 条件从多项式推广至斜广义幂级数，并推广了相关现有结果。

矩阵环和群环中单位的卷积码

Convolutional codes from units in matrix and group rings

本文给出了一种由矩阵环上Laurent级数的单位构造卷积码的一般方法。使用群环作为矩阵环，这形成了从群环编码深入探索卷积码的基础，其中群环中的环本身是群环。该方法被用来代数地构造卷积码系列。代数方法用于计算自由距离和构造规定距离的卷积码。

$\Bbb Z[t,t^{-1}]$上的有限模

Finite Modules over $\Bbb Z[t,t^{-1}]$

设$Λ=\Bbb Z[t,t^{-1}]$是$\Bbb Z$上的Laurent多项式环.我们用$|M|=p^n$对所有的$Λ$ -模$M$进行分类，其中$p$是素数，$n\le 4$是素数.因此，我们对$n\le 4$有一个$p^n$阶的Alexander量子点的分类。