Journal of Algebra最新文献

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Rings whose subrings are all Noetherian or Artinian 子环都是诺埃尔或阿提尼安的

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.jalgebra.2026.01.021

Nathan Blacher

We study noncommutative rings whose proper subrings all satisfy the same chain condition. We show that if every proper subring of a ring R is right Noetherian, then R is either right Noetherian or the trivial extension of

Z

by the Prüfer p-group for a prime p. We also prove that if every proper subring of R is right Artinian, then R is either right Artinian or

Z

. For commutative rings, both results were proved by Gilmer and Heinzer in 1992. Our result for right Artinian subrings only generalises the absolute case of their commutative result. We generalise the full result (when only certain subrings are right Artinian) in the context of PI rings.

研究了固有子环都满足同一链条件的非交换环。我们证明了如果环R的每个真子都是右noether的，那么R要么是右noether的，要么是Z被pr - p群对素数p的平凡扩展。我们还证明了如果R的每个真子都是右Artinian的，那么R要么是右Artinian的，要么是Z。对于交换环，Gilmer和Heinzer在1992年证明了这两个结果。我们对右阿提宁子带的结果只推广了它们的交换结果的绝对情况。我们在PI环的背景下推广了完整的结果（当只有某些子带是正确的）。

引用次数: 0

On squarefree powers of simplicial trees 关于简单树的无平方幂

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-19 DOI: 10.1016/j.jalgebra.2026.01.008

Elshani Kamberi, Francesco Navarra, Ayesha Asloob Qureshi

In this article, we study the squarefree powers of facet ideals associated with simplicial trees. Specifically, we examine the linearity of their minimal free resolution and their regularity. Additionally, we investigate when the first syzygy module of squarefree powers of facet ideal of a simplicial tree is generated by linear relations. Finally, we provide a combinatorial formula for the regularity of the squarefree powers of t-path ideals of path graphs.

在本文中，我们研究了与简单树相关的面理想的无平方幂。具体地说，我们研究了它们的最小自由分辨率的线性和它们的规律性。此外，我们还研究了简单树的面理想的无平方幂的第一个合模是什么时候由线性关系产生的。最后，我们给出了路径图的t路径理想的无平方幂的正则性的组合公式。

引用次数: 0

Prismatic Kunz's theorem 棱镜孔兹定理

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-19 DOI: 10.1016/j.jalgebra.2026.01.010

Ryo Ishizuka , Kei Nakazato

In this paper, we prove “prismatic Kunz's theorem” which states that a complete Noetherian local ring R of residue characteristic p is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) R over a specific prism

(A, I)

is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the “Frobenius map” to mixed characteristic rings. Our approach involves studying the deformation problem of the “regularity” of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex.

本文证明了剩馀特征为p的完全Noetherian局部环R是正则局部环的“棱镜Kunz定理”，当且仅当特定棱镜（a，I）上的棱镜复合体（R的一个推导增强）上的Frobenius升力是完全平坦的。从将“Frobenius映射”推广到混合特征环的角度对经典Kunz定理进行了推广。我们的方法包括研究棱镜的“规则性”变形问题，并展示棱镜复合体结构图的忠实平面性。

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 : 2026-05-01 Epub 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

Rationality patterns 理性模式

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-19 DOI: 10.1016/j.jalgebra.2026.01.013

Takuma Hayashi

In this paper, we establish general categorical frameworks that extend Loewy's classification scheme for finite-dimensional real irreducible representations of groups and Borel–Tits' criterion for the existence of rational forms of representations of

\bar{F} \otimes_{F} G

for a connected reductive algebraic group G over a field F of characteristic zero and its algebraic closure

\bar{F}

. We also discuss applications of these general formalisms to the theory of Harish-Chandra modules, specifically to classify irreducible Harish-Chandra modules over fields F of characteristic zero and to identify smaller fields of definition of irreducible Harish-Chandra modules over

\bar{F}

, particularly in the case of cohomological irreducible essentially unitarizable modules.

本文建立了一般范畴框架，扩展了群有限维实不可约表示的Loewy分类方案和特征为0的域F上的连通可约代数群G及其代数闭包F¯上F¯⊗FG表示的有理形式存在的Borel-Tits准则。我们还讨论了这些一般形式在Harish-Chandra模理论中的应用，特别是对特征为零的域F上的不可约Harish-Chandra模进行了分类，并确定了F¯上不可约Harish-Chandra模定义的较小域，特别是在上同调不可约本质可一元模的情况下。

引用次数: 0

Set-theoretic complete intersection for smooth surfaces in a smooth affine algebra 光滑仿射代数中光滑曲面的集合论完全交

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-16 DOI: 10.1016/j.jalgebra.2025.12.026

Lisa Mandal, Md. Ali Zinna

In this article we prove the following results:

(1) A smooth surface in a smooth affine

{\overline{F}}_{p}

-algebra with trivial conormal bundle is a set theoretic complete intersection, if its class in the Grothendieck group is torsion.

(2) A smooth hypersurface in an affine variety of dimension

n \geq 3

over

{\overline{F}}_{p}

can be described set theoretically by

n - 1

equations.

本文证明了以下结果：(1)具有平凡正规束的光滑仿射F - p代数中的光滑曲面是集合论完全交，如果它在Grothendieck群中的类是挠性的。(2)在F - p上具有n≥3维仿射变换的光滑超曲面可以用n−1个方程在理论上集合描述。

引用次数: 0

Virtual first Betti number of GGS groups GGS组的虚拟第一贝蒂数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-14 DOI: 10.1016/j.jalgebra.2026.01.002

Andrew Ng

We observe a criterion for groups to have vanishing virtual first Betti number and use it to give infinitely many examples of torsion-free, finitely generated, residually finite groups which aren't virtually diffuse. This answers a question raised by Kionke and Raimbault.

我们观察了群具有消失虚第一贝蒂数的一个判据，并利用它给出了无限多非虚扩散的无扭、有限生成、剩余有限群的例子。这回答了Kionke和Raimbault提出的一个问题。

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 : 2026-05-01 Epub 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

Presentations for the ghost algebra and the label algebra 鬼代数和标签代数的介绍

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2026-05-01 Epub Date: 2026-01-19 DOI: 10.1016/j.jalgebra.2025.12.027

Madeline Nurcombe

The ghost algebra is a two-boundary extension of the Temperley–Lieb algebra, constructed recently via a diagrammatic presentation. The existing two-boundary Temperley–Lieb algebra has a basis of two-boundary string diagrams, where the number of strings connected to each boundary must be even. The ghost algebra is similar, but allows this number to be odd, using bookkeeping dots called ghosts to assign a consistent parity to each string endpoint on each boundary. Equivalently, one can discard the ghosts and label each string endpoint with its parity; the resulting algebra is readily generalised to allow any number of possible labels, instead of just odd or even. We call the generalisation the label algebra, and establish a non-diagrammatic presentation for it. A similar presentation for the ghost algebra follows from this.

鬼代数是坦波利-利布代数的两边界扩展，最近通过图解表示构造。现有的两边界Temperley-Lieb代数具有两边界弦图的基础，其中连接到每个边界的弦数必须是偶数。鬼代数是类似的，但允许这个数字是奇数，使用称为鬼的记账点为每个边界上的每个字符串端点分配一致的奇偶校验。同样地，我们可以丢弃鬼影并用奇偶性标记每个字符串端点；由此产生的代数很容易推广到允许任何数量的可能标签，而不仅仅是奇数或偶数。我们称这种泛化为标签代数，并为其建立一种非图解表示。类似的关于鬼代数的表述也由此而来。

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 : 2026-05-01 Epub 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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