Journal of Algebra最新文献

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Deformations and homotopy theory of Nijenhuis associative algebras Nijenhuis结合代数的变形与同伦理论

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-29 DOI: 10.1016/j.jalgebra.2025.12.032

Chao Song , Kai Wang , Yuanyuan Zhang , Guodong Zhou

This paper is the first in a series of works devoted to an operadic study of Nijenhuis structures, focusing on Nijenhuis associative algebras. We introduce the concept of homotopy Nijenhuis associative algebras and demonstrate that the differential graded (=dg) operad

{NjA}_{\infty}

governing these structures serves as the minimal model of the operad

NjA

for Nijenhuis associative algebras. Additionally, we determine the Koszul dual homotopy cooperad of

NjA

. We construct an

L_{\infty}

-algebra that controls the simultaneous deformations of associative products and Nijenhuis operators. The Maurer-Cartan elements of this

L_{\infty}

-algebra correspond bijectively to Nijenhuis associative algebra structures. From this, we derive a cochain complex (deformation complex) and an associated cohomology theory of Nijenhuis associative algebras. Finally, we explore the connection between homotopy relative Rota-Baxter associative algebras of weight 0 and homotopy Nijenhuis associative algebras. A sequel to this work will extend the study to Nijenhuis Lie algebras, with applications to Nijenhuis geometry.

这篇论文是一系列致力于尼延惠斯结构的操作性研究的作品中的第一篇，重点是尼延惠斯结合代数。我们引入了同伦Nijenhuis结合代数的概念，并证明了控制这些结构的微分梯度（=dg）算子NjA∞作为Nijenhuis结合代数的算子NjA的最小模型。此外，我们还确定了NjA的Koszul对偶同伦。我们构造了一个L∞-代数来控制关联积和Nijenhuis算子的同时变形。该L∞代数的Maurer-Cartan元客观上对应于Nijenhuis联想代数结构。由此，我们得到了Nijenhuis结合代数的一个协链复形（变形复形）和一个相关上同调理论。最后，我们探讨了权值为0的同伦相对Rota-Baxter结合代数与同伦Nijenhuis结合代数之间的联系。这项工作的续集将把研究扩展到尼延惠斯李代数，并应用于尼延惠斯几何。

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引用次数: 0

Goto rings 转到环

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-29 DOI: 10.1016/j.jalgebra.2025.12.030

Naoki Endo

As part of stratification of Cohen-Macaulay rings, we introduce and develop the theory of Goto rings, generalizing the notion of almost Gorenstein rings originally defined by V. Barucci and R. Fröberg in 1997. What has dominated the series of researches on almost Gorenstein rings is the fact that the reduction numbers of extended canonical ideals are at most 2; we define Goto rings as Cohen-Macaulay rings admitting such extended canonical ideals. We provide a characterization of Goto rings in terms of the structure of Sally modules and determine the Hilbert functions of them. Various examples of Goto rings that come from numerical semigroups, idealizations, fiber products, and equimultiple Ulrich ideals are explored as well.

作为Cohen-Macaulay环分层的一部分，我们引入并发展了Goto环理论，推广了V. Barucci和R. Fröberg在1997年最初定义的几乎Gorenstein环的概念。在一系列关于几乎戈伦斯坦环的研究中占据主导地位的是这样一个事实：扩展正则理想的约化数最多为2；我们将Goto环定义为承认这种扩展规范理想的Cohen-Macaulay环。利用Sally模的结构给出了Goto环的一个表征，并确定了它们的Hilbert函数。从数值半群、理想化、纤维产物和等多重乌尔里希理想中探索了各种各样的后藤环的例子。

引用次数: 0

Khovanskii bases of subalgebras arising from finite distributive lattices 由有限分配格产生的子代数的Khovanskii基

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-29 DOI: 10.1016/j.jalgebra.2025.12.029

Akihiro Higashitani, Koji Matsushita , Koichiro Tani

The notion of Khovanskii bases was introduced by Kaveh and Manon [6]. It is a generalization of the notion of SAGBI bases for a subalgebra of polynomials. The notion of SAGBI bases was introduced by Robbiano and Sweedler [10] as an analogue of Gröbner bases in the context of subalgebras. A Hibi ideal is an ideal of a polynomial ring that arises from a distributive lattice. For the development of an analogy of the theory of Hibi ideals and Gröbner bases within the framework of subalgebras, in this paper, we investigate when the set of the polynomials associated with a distributive lattice forms a Khovanskii basis of the subalgebras it generates. We characterize such distributive lattices and their underlying posets. In particular, generalized snake posets and

{(2 + 2), (1 + 1 + 1)}

-free posets appear as the characterization.

Khovanskii基地的概念是由Kaveh和Manon提出的。它是多项式子代数SAGBI基概念的推广。SAGBI基的概念是由Robbiano和Sweedler[10]在子代数中作为Gröbner基的类比引入的。Hibi理想是由分配格产生的多项式环的理想。为了在子代数的框架内发展Hibi理想理论和Gröbner基的类比，本文研究了与分配格相关的多项式集何时形成它所生成的子代数的Khovanskii基。我们描述了这样的分配格及其潜在的偏置集。特别地，广义蛇形偏序集和{(2+2),(1+1+1)}自由偏序集作为表征出现。

引用次数: 0

Sylow subgroups for distinct primes and intersection of nilpotent subgroups 不同素数的Sylow子群与幂零子群的交

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-28 DOI: 10.1016/j.jalgebra.2025.12.028

Francesca Lisi, Luca Sabatini

Let G be a finite group and let

{(P_{i})}_{i = 1}^{n}

be Sylow subgroups for distinct primes

p_{1}, \dots, p_{n}

. We conjecture that there exists

x \in G

such that

P_{i} \cap P_{i}^{x}

is inclusion-minimal in

{P_{i} \cap P_{i}^{g} : g \in G}

for all i. As a first step in this direction, we show that a finite group cannot be covered by (proper) Sylow normalizers for distinct primes. Then we settle the conjecture in two opposite situations: symmetric and alternating groups of large degree and metanilpotent groups of odd order. Applications concerning the intersections of nilpotent subgroups are discussed.

设G是有限群，设（Pi）i=1n是不同素数p1，…，pn的Sylow子群。我们推测存在x∈G使得Pi∩Pix在{Pi∩Pig: G∈G}中对所有i都是最小包含。作为这个方向的第一步，我们证明了一个有限群不能被不同素数的（适当的）Sylow归一化器覆盖。然后我们在两种相反的情况下解决了这个猜想：大阶对称交替群和奇阶亚幂群。讨论了幂零子群交点的应用。

引用次数: 0

Some generalizations of Camina pairs and orders of elements in cosets Camina对的一些推广和集中元素的阶

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-27 DOI: 10.1016/j.jalgebra.2026.01.022

Thu T.H. Quan, Hung P. Tong-Viet

In this paper, we investigate certain generalizations of Camina pairs. Let H be a nontrivial proper subgroup of a finite group G. We first show that every nontrivial irreducible complex character of H induces homogeneously to G if and only if for every

x \in G ∖ H

, the element x is conjugate to xh for all

h \in H

. Furthermore we prove that if xh is conjugate to either x or

x^{- 1}

for all

h \in H

and all

x \in G ∖ H

, then the normal closure N of H in G also satisfies the same condition, and N is nilpotent. Finally, we determine the structure of H under the assumption that for every element

x \in G ∖ H

of odd order, the coset xH consists entirely of elements of odd order.

本文研究了Camina对的一些推广。设H是有限群G的一个非平凡的固有子群。首先证明H的每一个非平凡的不可约复特征齐次地归纳为G，当且仅当对于每一个x∈G∈H，元素x共轭于所有H∈H的xh。进一步证明了对于所有h∈h和所有x∈G∈h，如果xh共轭于x或x−1，则h在G中的正规闭包N也满足同样的条件，且N是幂零的。最后，在假设对于每一个奇阶元素x∈G∈H，余集xH完全由奇阶元素组成的前提下，我们确定了H的结构。

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引用次数: 0

Yet another differential shape lemma 另一个微分形状引理

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-22 DOI: 10.1016/j.jalgebra.2026.01.014

Joris van der Hoeven, Gleb Pogudin

Recently, Kauers, Koutschan, and Verron proved a non-commutative version of the classical shape lemma in the theory of Gröbner bases. Their result requires the ideal to be D-radical. In this note, we prove a new non-commutative shape lemma that does not require this assumption.

最近，Kauers， Koutschan和Verron证明了Gröbner基理论中经典形状引理的非交换版本。他们的结果要求理想是d基。在这篇笔记中，我们证明了一个新的非交换形状引理，它不需要这个假设。

引用次数: 0

Non-side-to-side tilings of the sphere by congruent triangles with an irrational angle 球面由具有无理角的全等三角形进行的非边对边的平铺

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-21 DOI: 10.1016/j.jalgebra.2026.01.003

Jinjin Liang, Wen Chen, Erxiao Wang

We develop the basic and new tools for classifying non-side-to-side tilings of the sphere by congruent triangles. Then we prove that, if the triangle has any irrational angle in degree, such tilings are: a sequence of 1-parameter families of triangles each admitting many 2-layer earth map tilings with 2n(

n \geq 3

) tiles, together with rotational modifications for even n; a 1-parameter family of triangles each admitting a unique tiling with 8 tiles; and a sporadic triangle admitting a unique tiling with 16 tiles. Then a scheme is outlined to classify the case with all angles being rational in degree, justified by some known and new examples.

我们开发了一种基本的和新的工具，用于用全等三角形来分类球面的非边对边平铺。然后，我们证明了，如果三角形在度数上有任何不合理的角度，这样的贴图是：一个1参数的三角形族序列，每个三角形族允许许多2n（n≥3）个贴图的2层地球地图贴图，并对偶数n进行旋转修改；一个1参数的三角形族，每个三角形都有一个独特的8个瓷砖；还有一个零星的三角形，有16块独特的瓷砖。在此基础上，提出了一种从各个角度进行合理分类的方案，并通过一些已知的和新的实例进行了论证。

引用次数: 0

Henselian schemes in positive characteristic 正特征的Henselian方案

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-21 DOI: 10.1016/j.jalgebra.2026.01.020

Sheela Devadas

The global analogue of a Henselian local ring is a Henselian pair: a ring A and an ideal I which satisfy a condition resembling Hensel's lemma regarding lifting coprime factorizations of polynomials over

A / I

to factorizations over A. The geometric counterpart is the notion of a Henselian scheme, which is an analogue of a tubular neighborhood in algebraic geometry.

In this paper we revisit the foundations of the theory of Henselian schemes. The pathological behavior of quasi-coherent sheaves on Henselian schemes in characteristic 0 makes them poor models for an “algebraic tube” in characteristic 0. We show that such problems do not arise in positive characteristic, and establish good properties for analogues of smooth and étale maps in the general Henselian setting.

Henselian局部环的全局类似物是一个Henselian对：一个环a和一个理想I，它们满足一个类似于Hensel引理的条件，这个引理是关于将a /I上的多项式的素分解提升到a上的因数分解。几何对应物是Henselian方案的概念，它是代数几何中管状邻域的类似物。本文回顾了Henselian格式理论的基础。特征为0的Henselian格式上的拟相干束的病态行为使其成为特征为0的“代数管”的不良模型。我们证明了在正特征中不会出现这样的问题，并在一般的Henselian环境中建立了光滑图和栅格图的类似物的良好性质。

引用次数: 0

Hyperplane arrangements and Vinberg's θ-groups 超平面排列和Vinberg的θ-群

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-21 DOI: 10.1016/j.jalgebra.2025.12.023

Filippo Ambrosio , Andrea Santi

Let

g = ⨁_{i \in Z / m Z} g_{i}

be a periodically graded semisimple complex Lie algebra. In this note, we give a uniform proof of the recent result by W. de Graaf and H. V. Lê that the hyperplane arrangement determined by the restrictions of the roots of

g

to a Cartan subspace

c \subset g_{1}

coincides with the hyperplane arrangement of (complex) reflections of the little Weyl group of

g = ⨁_{i \in Z / m Z} g_{i}

设g= φ i∈Z/mZgi是一个周期渐变的半简单复李代数。在本文中，我们统一证明了W. de Graaf和H. V. Lê最近的结果，即由g的根对Cartan子空间c∧g1的限制所决定的超平面排列与g= i∈Z/mZgi的小Weyl群的（复）反射的超平面排列是一致的。

引用次数: 0

On the solutions of the generalized Fermat equation over totally real number fields 全实数域上广义费马方程的解

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-01-21 DOI: 10.1016/j.jalgebra.2026.01.006

Satyabrat Sahoo

Let K be a totally real number field and

O_{K}

be the ring of integers of K. In this article, we study the asymptotic solutions of the generalized Fermat equation, namely

A x^{p} + B y^{p} + C z^{p} = 0

over K with prime exponent p, where

A, B, C \in O_{K} ∖ {0}

with ABC is even. For certain class of fields K, we prove that the equation

A x^{p} + B y^{p} + C z^{p} = 0

has no asymptotic solution

(a, b, c) \in O_{K}^{3}

with

2 | a b c

. Then, under some assumptions on

A, B, C

, we also prove that

A x^{p} + B y^{p} + C z^{p} = 0

has no asymptotic solution in

K^{3}

. Finally, we give several purely local criteria of K such that

A x^{p} + B y^{p} + C z^{p} = 0

has no asymptotic solutions in

K^{3}

, and calculate the density of such fields K when K is a real quadratic field.

设K为全实数域，OK为K的整数环。本文研究了具有素数指数p的广义费马方程Axp+Byp+Czp=0 / K的渐近解，其中a，B,C∈OK∈{0}，ABC为偶。对于某类域K，证明了方程Axp+Byp+Czp=0在2|abc下无渐近解(a,b,c)∈OK3。然后，在A，B，C的某些假设下，证明了Axp+Byp+Czp=0在K3中无渐近解。最后，给出了Axp+Byp+Czp=0在K3中无渐近解的几个纯局部判据，并计算了K为实二次域时该类场K的密度。

引用次数: 0

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