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arXiv: Rings and Algebras最新文献

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A Survey on the Ideal Structure of Leavitt Path Algebras 莱维特路径代数的理想结构研究
arXiv: Rings and Algebras Pub Date : 2018-10-19 DOI: 10.1007/978-981-15-1611-5_5
M. Kanuni, Suat Sert
{"title":"A Survey on the Ideal Structure of Leavitt Path Algebras","authors":"M. Kanuni, Suat Sert","doi":"10.1007/978-981-15-1611-5_5","DOIUrl":"https://doi.org/10.1007/978-981-15-1611-5_5","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114566235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces 无穷维向量空间上一些线性映射的Moore-Penrose逆
arXiv: Rings and Algebras Pub Date : 2018-10-09 DOI: 10.13001/ela.2020.4979
V. S'anchez, F. P. Romo
{"title":"Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces","authors":"V. S'anchez, F. P. Romo","doi":"10.13001/ela.2020.4979","DOIUrl":"https://doi.org/10.13001/ela.2020.4979","url":null,"abstract":"The aim of this work is to characterize linear maps of inner pro-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $Ain text{Mat}_{ntimes m} ({mathbb C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, we study the least norm solution of an infinite linear system from the Moore-Penrose inverse offered.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"299 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129313234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Third-Order Jacobsthal Generalized Quaternions 三阶jacobthal广义四元数
arXiv: Rings and Algebras Pub Date : 2018-10-07 DOI: 10.7546/jgsp-50-2018-11-27
Gamaliel Cerda-Morales
{"title":"Third-Order Jacobsthal Generalized Quaternions","authors":"Gamaliel Cerda-Morales","doi":"10.7546/jgsp-50-2018-11-27","DOIUrl":"https://doi.org/10.7546/jgsp-50-2018-11-27","url":null,"abstract":"In this paper, the third-order Jacobsthal generalized quaternions are introduced. We use the well-known identities related to the third-order Jacobsthal and third-order Jacobsthal-Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the third-order Jacobsthal generalized quaternions are classified by considering the special cases of quaternionic units. We derive the relations between third-order Jacobsthal and third-order Jacobsthal-Lucas generalized quaternions.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116962832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Dimer models and Hochschild cohomology 二聚体模型与Hochschild上同调
arXiv: Rings and Algebras Pub Date : 2018-08-15 DOI: 10.15781/T2NS0MH1J
M. Wong
{"title":"Dimer models and Hochschild cohomology","authors":"M. Wong","doi":"10.15781/T2NS0MH1J","DOIUrl":"https://doi.org/10.15781/T2NS0MH1J","url":null,"abstract":"Dimer models provide a method of constructing noncommutative crepant resolutions of affine toric Gorenstein threefolds. In homological mirror symmetry, they can also be used to describe noncommutative Landau--Ginzburg models dual to punctured Riemann surfaces. For a zigzag consistent dimer embedded in a torus, we explicitly compute the Hochschild cohomology of its Jacobi algebra in terms of dimer combinatorics. This includes a full characterization of the Batalin--Vilkovisky structure induced by the Calabi--Yau structure of the Jacobi algebra. We then compute the compactly supported Hochschild cohomology of the category of matrix factorizations for the Jacobi algebra with its canonical potential.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130455214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Problems on skew left braces 左斜括号的问题
arXiv: Rings and Algebras Pub Date : 2018-07-17 DOI: 10.32037/agta-2019-003
L. Vendramin
{"title":"Problems on skew left braces","authors":"L. Vendramin","doi":"10.32037/agta-2019-003","DOIUrl":"https://doi.org/10.32037/agta-2019-003","url":null,"abstract":"Braces were introduced by Rump as a generalization of Jacobson radical rings. It turns out that braces allow us to use ring-theoretic and group-theoretic methods for studying involutive solutions to the Yang-Baxter equation. If braces are replaced by skew braces, then one can use similar methods for studying not necessarily involutive solutions. Here we collect problems related to (skew) braces and set-theoretic solutions to the Yang-Baxter equation.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128031302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 31
A proof of the elliptical range theorem via Kippenhahn's theorem 用Kippenhahn定理证明椭圆范围定理
arXiv: Rings and Algebras Pub Date : 2018-07-11 DOI: 10.35834/2021/3302181
Pietro Paparella, L. J. Ramirez, Yen-Fen Wang
{"title":"A proof of the elliptical range theorem via Kippenhahn's theorem","authors":"Pietro Paparella, L. J. Ramirez, Yen-Fen Wang","doi":"10.35834/2021/3302181","DOIUrl":"https://doi.org/10.35834/2021/3302181","url":null,"abstract":"The elliptical range theorem asserts that the field of values (or numerical range) of a two-by-two matrix with complex entries is an elliptical disk, the foci of which are the eigenvalues of the given matrix. Many proofs of this result are available in the literature, but most, with one exception, are computational and quite involved. In this note, it is shown that the elliptical range theorem follows from the properties of plane algebraic curves and a straightforward application of a well-known result due to Kippenhahn.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126028570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vertex and Edge connectivity of the zero divisor graph $Gamma[mathbb {Z}_n]$. 零因子图$Gamma[mathbb {Z}_n]$的顶点和边连通性。
arXiv: Rings and Algebras Pub Date : 2018-07-07 DOI: 10.26713/CMA.V11I2.1319
B. Reddy, Rupali.S.Jain, N.Laxmikanth
{"title":"Vertex and Edge connectivity of the zero divisor graph $Gamma[mathbb {Z}_n]$.","authors":"B. Reddy, Rupali.S.Jain, N.Laxmikanth","doi":"10.26713/CMA.V11I2.1319","DOIUrl":"https://doi.org/10.26713/CMA.V11I2.1319","url":null,"abstract":"The Zero divisor Graph of a commutative ring $R$, denoted by $Gamma[R]$, is a graph whose vertices are non-zero zero divisors of $R$ and two vertices are adjacent if their product is zero. In this paper we derive the Vertex and Edge Connectivity of the zero divisor graph $Gamma[mathbb{Z}_n]$, for any natural number $n$ . We also discuss the minimum degree of the zero divisor graph $Gamma[mathbb{Z}_n]$.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131647068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Defining relations of 3-dimensional quadratic AS-regular algebras 定义三维二次as正则代数的关系
arXiv: Rings and Algebras Pub Date : 2018-06-13 DOI: 10.18926/mjou/60866
Ayako Itaba, Masaki Matsuno
{"title":"Defining relations of 3-dimensional quadratic AS-regular algebras","authors":"Ayako Itaba, Masaki Matsuno","doi":"10.18926/mjou/60866","DOIUrl":"https://doi.org/10.18926/mjou/60866","url":null,"abstract":"Classification of AS-regular algebras is one of the main interests in non-commutative algebraic geometry. Recently, a complete list of superpotentials (defining relations) of all $3$-dimensional AS-regular algebras which are Calabi-Yau was given by Mori-Smith (the quadratic case) and Mori-Ueyama (the cubic case), however, no complete list of defining relations of all $3$-dimensional AS-regular algebras has not appeared in the literature. In this paper, we give all possible defining relations of $3$-dimensional quadratic AS-regular algebras. Moreover, we classify them up to isomorphism and up to graded Morita equivalence in terms of their defining relations in the case that their point schemes are not elliptic curves. In the case that their point schemes are elliptic curves, we give conditions for isomorphism and graded Morita equivalence in terms of geometric data.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129876738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Embedding of Quadratic Spaces 二次空间的嵌入
arXiv: Rings and Algebras Pub Date : 2018-05-07 DOI: 10.25537/dm.2018v23.1621-1634
Vineeth Chintala
{"title":"Embedding of Quadratic Spaces","authors":"Vineeth Chintala","doi":"10.25537/dm.2018v23.1621-1634","DOIUrl":"https://doi.org/10.25537/dm.2018v23.1621-1634","url":null,"abstract":"We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard involution and the Spin groups in terms of the algebra in which the quadratic space is embedded. \u0000Though Clifford Algebras have been studied in detail, they may not always be easy to work with. Sometimes it may be useful to switch to a more concrete embedding to study low dimensional Spin and Epin (or Elementary Spin) groups.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115739992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
NILPOTENT MODULES OVER POLYNOMIAL RINGS 多项式环上的幂零模
arXiv: Rings and Algebras Pub Date : 2018-05-02 DOI: 10.17721/1684-1565.2020.01-41.06.20-25
I. Chapovskyi, A. Petravchuk
{"title":"NILPOTENT MODULES OVER POLYNOMIAL RINGS","authors":"I. Chapovskyi, A. Petravchuk","doi":"10.17721/1684-1565.2020.01-41.06.20-25","DOIUrl":"https://doi.org/10.17721/1684-1565.2020.01-41.06.20-25","url":null,"abstract":"Let $mathbb K$ be an algebraically closed field of characteristic zero, $mathbb K[X]$ the polynomial ring in $n$ variables. The vector space $T_n = mathbb K[X]$ is a $mathbb K[X]$-module with the action $x_i cdot v = v_{x_i}'$ for $v in T_n$. Every finite dimensional submodule $V$ of $T_n$ is nilpotent, i.e. every polynomial $f in mathbb K[X]$ with zero constant term acts nilpotently (by multiplication) on $V.$ We prove that every nilpotent $mathbb K[X]$-module $V$ of finite dimension over $mathbb K$ with one dimensional socle can be isomorphically embedded in the module $T_n$. The automorphism groups of the module $T_n$ and its finite dimensional monomial submodules are found. Similar results are obtained for (non-nilpotent) finite dimensional $mathbb K[X]$-modules with one dimensional socle.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125261884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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