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Rota---Baxter operators on $Cur(sl_2(mathbb{C}))$ Rota—$Cur(sl_2(mathbb{C}))$上的Baxter运算符
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-12-13 DOI: 10.24330/ieja.1218727
V. Gubarev, R. Kozlov
We classify all Rota---Baxter operators on the simple Lie conformal algebra $Cur(sl_2(mathbb{C}))$ and clarify which of them arise from the solutions to the conformal classical Yang---Baxter equation due to the connection discovered by Y. Hong and C. Bai in 2020.
我们对简单Lie共形代数$Cur(sl_2(mathbb{C}))$上的所有Rota—Baxter算子进行了分类,并澄清了其中哪些算子是由Y. Hong和C. Bai在2020年发现的共形经典Yang—Baxter方程的解产生的。
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引用次数: 0
When do quasi-cyclic codes have $mathbb F_{q^l}$-linear image? 什么时候准循环码有$mathbb F_{q^l}$-线性图像?
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-11-01 DOI: 10.24330/ieja.1198011
R. Nekooei, Z. Pourshafiey
A length $ml$, index $l$ quasi-cyclic code can be viewed as a cyclic code of length $m$ over the field $mathbb F_{q^l}$ via a basis of the extension $mathbb F_{q^l}/mathbb F_{q}$. This cyclic code is an additive cyclic code. In [C. Güneri, F. Özdemir, P. Solé, On the additive cyclic structure of quasi-cyclic codes, Discrete. Math., 341 (2018), 2735-2741], authors characterize the $(l,m)$ values for one-generator quasi-cyclic codes for which it is impossible to have an $mathbb F_{q^l}$-linear image for any choice of the polynomial basis of $mathbb F_{q^l}/mathbb F_{q}$. But this characterization for some $(l,m)$ values is very intricate. In this paper, by the use of this characterization, we give a more simple characterization.
一个长度$ml$,索引$l$的准循环码可以看作是一个长度$m$的循环码,通过扩展$mathbb F_{q^l}/mathbb F_{q}$的基,在字段$mathbb F_{q}$上。这个循环码是一个加性循环码。在[C。g neri, F. Özdemir, P. sol,关于拟循环码的加性循环结构,离散。数学。对于任意选择$mathbb F_{q^l}/mathbb F_{q}$的多项式基,都不可能有$mathbb F_{q}$线性图像的一元拟循环码,[j], 341(2018), 2735-2741],作者刻画了$(l,m)$值。但是对于某些$(l,m)$值,这种表征是非常复杂的。在本文中,利用这一表征,我们给出了一个更简单的表征。
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引用次数: 0
Cayley subspace sum graph of vector spaces 向量空间的Cayley子空间和图
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-10-27 DOI: 10.24330/ieja.1195466
G. Kalaimurugan, S. Gopinath, T. Tamizh Chelvam
Let $mathbb{V}$ be a finite dimensional vector space over the field $mathbb{F}$. Let $S(mathbb{V})$ be the set of all subspaces of $mathbb{V}$ and $mathbb{A}subseteq S^*(mathbb{V})=S(mathbb{V})backslash{0}.$ In this paper, we define the Cayley subspace sum graph of $mathbb{V},$ denoted by Cay$(S^*(mathbb{V}),mathbb{A}), $ as the simple undirected graph with vertex set $S^*(mathbb{V})$ and two distinct vertices $X$ and $Y$ are adjacent if $X+Z=Y$ or $Y+Z=X$ for some $Zin mathbb{A}$. Having defined the Cayley subspace sum graph, we study about the connectedness, diameter and girth of several classes of Cayley subspace sum graphs Cay$(S^*(mathbb{V}), mathbb{A})$ for a finite dimensional vector space $mathbb{V}$ and $mathbb{A}subseteq S^*(mathbb{V})=S(mathbb{V})backslash{0}.$
设$mathbb{V}$是域$mathbb{F}$上的有限维向量空间。设$S(mathbb{V})$是$mathbb{V}$和$mathbb{A}substeq S^*(mathbb{V})=S(mathbb{V{)反斜杠{0}的所有子空间的集合。$在本文中,我们定义了$mathbb{V},$的Cayley子空间和图,用Cay$(S^*(mathbb{V}),mathbb}A})表示,$是一个简单的无向图,其顶点集为$S^*(athbb{V}。在定义了Cayley子空间和图后,我们研究了有限维向量空间$mathbb{V}$和$mathbb{A}substeqS^*(mathbb{V})=S(mathbb{V})反斜杠的几类Cayley个子空间和图Cay$(S^*),mathbb(A})$的连通性、直径和周长$
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引用次数: 0
On modules with chain condition on non-small submodules 非小子模块上具有链条件的模块
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-10-27 DOI: 10.24330/ieja.1195509
A. K. Chaturvedi, Nirbhay Kumar
In 1979, Fleury studied a class of modules with finite spanning dimension and dually a class of modules with ascending chain condition on non-small submodules was studied by Lomp and Ozcan in 2011. In the present work, we explore and investigate some new characterizations and properties of these classes of modules.
1979年Fleury研究了一类生成维数有限的模,2011年Lomp和Ozcan研究了非小子模上具有升链条件的模。在本工作中,我们探索和研究了这类模块的一些新的表征和性质。
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引用次数: 0
On Generalized Probability in Finite Commutative Rings 有限交换环上的广义概率
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-08-05 DOI: 10.24330/ieja.1156662
S. Rehman, Muhammad Naveed Shaheryar
Let $R$ be a finite commutative ring with unity and $xin R$. We study the probability that the product of two randomly chosen elements (with replacement) of $R$ equals $x$. We denote this probability by $Prob_x (R)$. We determine some bounds for this probability and also obtain some characterizations of finite commutative rings based on this probability. Moreover, we determine the explicit computing formulas for $Prob_x (R)$ when $R=mathbb{Z}_mtimes mathbb{Z}_n$.
设$R$是一个有单位的有限交换环,且$x在R$中。我们研究了R$的两个随机选择的元素(有替换)的乘积等于x$的概率。我们用$Prob_x (R)$表示这个概率。我们确定了这个概率的一些界,并在此基础上得到了有限交换环的一些表征。此外,我们确定了当$R=mathbb{Z}_m乘以mathbb{Z}_n$时$Prob_x (R)$的显式计算公式。
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引用次数: 0
Planar index and outerplanar index of zero-divisor graphs of commutative rings without identity 无恒等交换环零除数图的平面索引和外平面索引
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-08-01 DOI: 10.24330/ieja.1152714
G. Kalaimurugan, P. Vignesh, M. Afkhami, Z. Barati
Let $R$ be a commutative ring without identity. The zero-divisor graph of $R,$ denoted by $Gamma(R)$ is a graph with vertex set $Z(R)setminus {0}$ which is the set of all nonzero zero-divisor elements of $R,$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0.$ In this paper, we characterize the rings whose zero-divisor graphs are ring graphs and outerplanar graphs. Further, we establish the planar index, ring index and outerplanar index of the zero-divisor graphs of finite commutative rings without identity.
设$R$是一个没有恒等式的交换环。用$Gamma(R)$表示的$R,$的零除数图是一个顶点集为$Z(R)setminus{0}$的图,它是$R,$$的所有非零零除数元素的集合,并且两个不同的顶点$x$和$y$是相邻的当且仅当$xy=0。进一步,我们建立了有限交换环的零除数图的平面索引、环索引和外平面索引。
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引用次数: 0
The structure of matrix polynomial algebras 矩阵多项式代数的结构
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-07-29 DOI: 10.24330/ieja.1151001
Bertrand Nguefack
This work formally introduces and starts investigating the structure of matrix polynomial algebra extensions of a coefficient algebra by (elementary) matrix-variables over a ground polynomial ring in not necessary commuting variables. These matrix subalgebras of full matrix rings over polynomial rings show up in noncommutative algebraic geometry. We carefully study their (one-sided or bilateral) noetherianity, obtaining a precise lift of the Hilbert Basis Theorem when the ground ring is either a commutative polynomial ring, a free noncommutative polynomial ring or a skew polynomial ring extension by a free commutative term-ordered monoid. We equally address the natural but rather delicate question of recognising which matrix polynomial algebras are Cayley-Hamilton algebras, which are interesting noncommutative algebras arising from the study of $mathrm{Gl}_{n}$-varieties.
这项工作正式引入并开始研究系数代数的矩阵多项式代数的结构——在不必要的交换变量中,通过地面多项式环上的(初等)矩阵变量来扩展系数代数。多项式环上的全矩阵环的这些矩阵子代数表现在非对易代数几何中。我们仔细研究了它们(单侧或双侧)的非对称性,得到了当地环是交换多项式环、自由非对易多项式环或由自由交换项有序半群扩展的斜多项式环时希尔伯特基定理的精确提升。我们同样解决了一个自然但相当微妙的问题,即识别哪些矩阵多项式代数是Cayley-Hamilton代数,它们是由$mathrm的研究产生的有趣的非交换代数{Gl}_{n} $-品种。
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引用次数: 0
Lie structure of the Heisenberg-Weyl algebra Heisenberg—Weyl代数的李结构
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-07-25 DOI: 10.24330/ieja.1326849
R. Cantuba
As an associative algebra, the Heisenberg--Weyl algebra $HWeyl$ is generated by two elements $A$, $B$ subject to the relation $AB-BA=1$. As a Lie algebra, however, where the usual commutator serves as Lie bracket, the elements $A$ and $B$ are not able to generate the whole space $HWeyl$. We identify a non-nilpotent but solvable Lie subalgebra $coreLie$ of $HWeyl$, for which, using some facts from the theory of bases for free Lie algebras, we give a presentation by generators and relations. Under this presentation, we show that, for some algebra isomorphism $isoH:HWeylintoHWeyl$, the Lie algebra $HWeyl$ is generated by the generators of $coreLie$, together with their images under $isoH$, and that $HWeyl$ is the sum of $coreLie$, $isoH(coreLie)$ and $lbrak coreLie,isoH(coreLie)rbrak$.
Heisenberg—Weyl代数$HWeyl$是由两个元素$A$, $B$根据关系$AB-BA=1$生成的。然而,作为李代数,通常的换向子作为李括号,元素$ a $和$B$不能生成整个空间$HWeyl$。利用自由李代数基论中的一些事实,利用生成子和关系式给出了一个非幂零但可解的李子代数。本文证明,对于一些代数同构$isoH:HWeyl到$ HWeyl$,李代数$HWeyl$是由$coreLie$的生成器及其$coreLie$下的图像生成的,并且$HWeyl$是$coreLie$, $isoH(coreLie)$和$lbrak coreLie,isoH(coreLie) $和$lbrak coreLie,isoH(coreLie)rbrak$的和。
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引用次数: 0
Fields whose torsion free parts divisible with trivial Brauer group 无扭转部分可被平凡Brauer群整除的域
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-07-15 DOI: 10.24330/ieja.1144156
R. Fallah-Moghaddam
Let $F_0$ be an absolutely algebraic field of characteristic $p>0$ and $kappa$ an infinite cardinal. It is shown that there exists a field $F$ such that $F^*cong F^*_0oplus(oplus_kappa mathbb{Q})$ with $Br(F)={0}$. Let $L$ be an algebraic closure of $F$. Then for any finite subextension $K$ of $L/F$, we have $K^*cong T(K^*)oplus(oplus_kappa mathbb{Q})$, where $T(K^*)$ is the group of torsion elements of $K^*$. In addition, $Br(K)={0}$ and $[K:F]=[T(K^*) cup {0}:F_0]$.
设$F_0$为特征为$p>0$的绝对代数域,$kappa$为无限基数。结果表明,存在一个域$F$,使得$F^*cong F^*_0oplus(oplus_kappa mathbb{Q})$与$Br(F)={0}$。设$L$为$F$的代数闭包。然后对于$L/F$的任意有限子扩展$K$,我们有$K^*cong T(K^*)oplus(oplus_kappa mathbb{Q})$,其中$T(K^*)$是$K^*$的扭转单元群。此外,还有$Br(K)={0}$和$[K:F]=[T(K^*) cup {0}:F_0]$。
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引用次数: 0
On solubility of groups with finitely many centralizers 关于具有有限多个中心子的群的溶解度
IF 0.6 Q3 MATHEMATICS Pub Date : 2022-07-15 DOI: 10.24330/ieja.1144159
I. Lima, Caio Rodrigues
In this paper we present a new sufficient condition for a solubility criterion in terms of centralizers of elements. This result is a corrigendum of one of Zarrin's results. Furthermore, we extend some of K. Khoramshahi and M. Zarrin's results in the primitive case.
本文给出了关于元素中心化剂的溶解度判据的一个新的充分条件。这个结果是对Zarrin的一个结果的更正。此外,我们推广了K. Khoramshahi和M. Zarrin在原始情况下的一些结果。
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International Electronic Journal of Algebra
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