Journal of Algebra and Its Applications最新文献

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Morita equivalence and globalization for partial Hopf actions on nonunital algebras 莫里塔等价性与非空格布拉上部分霍普夫作用的全局化

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-05-17 DOI: 10.1142/s0219498825502627

Marcelo Muniz Alves, Tiago Luiz Ferrazza

In this work, we investigate partial actions of a Hopf algebra $H$ on nonunital algebras and the associated partial smash products, with the objective of providing a framework where one may obtain results for both $𝕜$ -algebras with local units and $𝕜$ -categories. We show that our partial actions correspond to nonunital algebras in the category of partial representations of $H$ . The central problem of existence of a globalization for a partial action is studied in detail, and we provide sufficient conditions for the existence (and uniqueness) of a minimal globalization for associative algebras in general. Extending previous results by Abadie, Dokuchaev, Exel and Simon, we define Morita equivalence for partial Hopf actions, and we show that if two symmetrical partial actions are Morita equivalent then their standard globalizations are also Morita equivalent. Particularizing to the case of a partial action on an algebra with local units, we obtain several strong results on equivalences of categories of modules of partial smash products of algebras and partial smash products of $𝕜$ -categories.

在这篇论文中，我们研究了霍普夫代数 H 在非空格代数上的部分作用以及相关的部分粉碎乘积，目的是提供一个框架，在这个框架中，我们既可以得到有局部单元的𝕜代数的结果，也可以得到𝕜范畴的结果。我们详细研究了部分作用的全局化存在性这一核心问题，并为一般关联代数的最小全局化的存在性（和唯一性）提供了充分条件。我们扩展了阿巴迪、多库恰耶夫、埃塞尔和西蒙以前的成果，定义了部分霍普夫作用的莫里塔等价性，并证明如果两个对称的部分作用是莫里塔等价的，那么它们的标准全局化也是莫里塔等价的。特别是在具有局部单元的代数上的部分作用的情况下，我们得到了关于代数的部分粉碎乘积的模块类别和𝕜类别的部分粉碎乘积的等价性的几个强有力的结果。

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引用次数: 0

Wilf inequality is preserved under gluing of semigroups Wilf 不等式在半群胶合时得到保留

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-26 DOI: 10.1142/s021949882550255x

Srishti Singh, Hema Srinivasan

Wilf Conjecture on numerical semigroups is a question posed by Wilf in 1978 and is an inequality connecting the Frobenius number, embedding dimension and the genus of the semigroup. The conjecture is still open in general. We prove that this Wilf inequality is preserved under gluing of numerical semigroups. If the numerical semigroups minimally generated by $A = {a_{1}, \dots, a_{p}}$ and $B = {b_{1}, \dots, b_{q}}$ satisfy the Wilf inequality, then so does their gluing which is minimally generated by $C = k_{1} A ⊔ k_{2} B$ . We discuss the extended Wilf’s Conjecture in higher dimensions for certain affine semigroups and prove an analogous result.

关于数值半群的 Wilf 猜想是 Wilf 于 1978 年提出的一个问题，是连接半群的弗罗贝尼斯数、嵌入维数和属数的不等式。该猜想在一般情况下仍未解决。我们证明，这个 Wilf 不等式在数字半群的胶合作用下得以保留。如果由 A={a1,...ap} 和 B={b1,...bq} 最小生成的数字半群满足 Wilf 不等式，那么由 C=k1A⊔k2B 最小生成的它们的胶合也满足 Wilf 不等式。我们讨论了某些仿射半群在更高维度上的扩展 Wilf 猜想，并证明了一个类似的结果。

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引用次数: 0

Graver bases of shifted numerical semigroups with 3 generators 有 3 个发电机的移位数字半群的格拉弗基

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-20 DOI: 10.1142/s0219498825502275

James Howard, Christopher O’Neill

A numerical semigroup $M$ is a subset of the non-negative integers that is closed under addition. A factorization of $n \in M$ is an expression of $n$ as a sum of generators of $M$ , and the Graver basis of $M$ is a collection $Gr (M_{t})$ of trades between the generators of $M$ that allows for efficient movement between factorizations. Given positive integers $r_{1}, \dots, r_{k}$ , consider the family $M_{t} = 〈 t + r_{1}, \dots, t + r_{k}$ of “shifted” numerical semigroups whose generators are obtained by translating $r_{1}, \dots, r_{k}$ by an integer parameter $t$ . In this paper, we characterize the Graver basis $Gr (M_{t})$ of $M_{t}$ for sufficiently large $t$ in the case

数字半群 M 是非负整数的一个子集，在加法运算下是封闭的。n∈M 的因式分解是 n 作为 M 的生成器之和的表达式，而 M 的格雷弗基是 M 的生成器之间的交易集合 Gr(Mt)，它允许因式分解之间的有效移动。给定正整数 r1,...,rk，考虑 "移位 "数字半群 Mt 系列=〈t+r1,...,t+rk，其生成器通过将 r1,...,rk平移一个整数参数 t 而获得。在本文中，我们从较小 t 值的 Gr(Mt)出发，以递归构造的形式，描述了在 k=3 的情况下，足够大 t 的 Mt 的格雷弗基 Gr(Mt)。我们还得到了准线性行为开始时的一个尖锐下限。

引用次数: 0

On 2-Absorbing Ideals Of Non-Commutative Semirings 论非交换半irings 的 2-Absorbing Ideals

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-18 DOI: 10.1142/s0219498825502780

Mohammad Adarbeh, Mohammad Saleh

引用次数: 0

The Dual Vector Spaces of Symmetric Tensor Powers of Composition Algebras 组合代数的对称张量幂的对偶向量空间

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-18 DOI: 10.1142/s0219498825502779

A. Razon

引用次数: 0

Relationships between Almost Completely Decomposable Abelian Groups and Their Multiplication Groups 几乎可完全分解的阿贝尔群及其乘法群之间的关系

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-18 DOI: 10.1142/s0219498825502755

E. Kompantseva, Askar Tuganbaev

引用次数: 0

On the Graded Injective Hull of R/𝔭 in Prime Characteristic 论素性 R/𝔭 的分级注入体

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-18 DOI: 10.1142/s0219498825502810

Aarti Patle, Jyoti Singh

引用次数: 0

The primeness of noncommutative polynomials on prime rings 素环上非交换多项式的原始性

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-18 DOI: 10.1142/s0219498825502767

M. Tamer Koşan, Tsiu-Kwen Lee

引用次数: 0

The Boomerang Uniformity of Three Classes of Permutation Polynomials over 𝔽2n 𝔽2n上三类置换多项式的回旋均匀性

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-18 DOI: 10.1142/s0219498825502792

Qian Liu, Zhixiong Chen, Ximeng Liu

引用次数: 0

Cohomology and the controlling algebra of crossed homomorphisms on 3-Lie algebras 同调与 3-李代数上交叉同态的控制代数

IF 0.8 3区数学 Q2 Mathematics

Journal of Algebra and Its Applications

Pub Date : 2024-04-17 DOI: 10.1142/s0219498825502317

Shuai Hou, Meiyan Hu, Lina Song, Yanqiu Zhou

In this paper, first we give the notion of a crossed homomorphism on a $3$ -Lie algebra with respect to an action on another $3$ -Lie algebra, and characterize it using a homomorphism from a 3-Lie algebra to the semidirect product 3-Lie algebra. We also establish the relationship between crossed homomorphisms and relative Rota–Baxter operators of weight $1$ on 3-Lie algebras. Next we construct a cohomology theory for a crossed homomorphism on $3$ -Lie algebras and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Finally, using the higher derived brackets, we construct an $L_{\infty}$ -algebra whose Maurer–Cartan elements are crossed homomorphisms. Consequently, we obtain the twisted $L_{\infty}$ -algebra that controls deformations of a given crossed homomorphism on $3$ -Lie algebras.

在本文中，我们首先给出了3-Lie代数上相对于另一个3-Lie代数上的作用的交叉同态的概念，并用从3-Lie代数到半直接积3-Lie代数的同态来描述它的特征。我们还建立了交叉同态与 3-Lie 代数上权重为 1 的相对 Rota-Baxter 算子之间的关系。接下来，我们构建了 3-Lie 代数上交叉同态的同调理论，并利用第二同调群对交叉同态的无限小变形进行了分类。最后，我们利用高阶导出括号，构造了一个 L∞-algebra ，其毛勒-卡尔坦元素是交叉同态。因此，我们得到了控制给定交叉同态在 3-Lie 代数上变形的扭曲 L∞-algebra 。

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引用次数: 0

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