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Three limit representations of the core-EP inverse 核心- ep逆的三种极限表示
arXiv: Rings and Algebras Pub Date : 2018-04-14 DOI: 10.2298/FIL1817887Z
Mengmeng Zhou, Jianlong Chen, Tingting Li, Ding-Guo Wang
{"title":"Three limit representations of the core-EP inverse","authors":"Mengmeng Zhou, Jianlong Chen, Tingting Li, Ding-Guo Wang","doi":"10.2298/FIL1817887Z","DOIUrl":"https://doi.org/10.2298/FIL1817887Z","url":null,"abstract":"In this paper, we present three limit representations of the core-EP inverse. The first approach is based on the full-rank decomposition of a given matrix. The second and third approaches, which depend on the explicit expression of the core-EP inverse, are established. The corresponding limit representations of the dual core-EP inverse are also given. In particular, limit representations of the core and dual core inverse are derived","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123448601","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: 32
Locally nilpotent Lie algebras of derivations of integral domains 整域导数的局部幂零李代数
arXiv: Rings and Algebras Pub Date : 2018-04-04 DOI: 10.15407/2457
A. Petravchuk, O. Shevchyk, K. Sysak
{"title":"Locally nilpotent Lie algebras of derivations of integral domains","authors":"A. Petravchuk, O. Shevchyk, K. Sysak","doi":"10.15407/2457","DOIUrl":"https://doi.org/10.15407/2457","url":null,"abstract":"Let K be a field of characteristic zero and A an integral domain over K . The Lie algebra Der K A of all K -derivations of A carries very important information about the algebra A . This Lie algebra is embedded into the Lie algebra R Der K A $subseteq$Der K R , where R =Frac( A ) is the fraction field of A . The rank rk R L of a subalgebra L of R Der K A is defined as dimension dim R RL . We prove that every locally nilpotent subalgebra L of R Der K A with rk R L = n has a series of ideals 0= L 0 ⊂ L 1 ⊂ L 2 …⊂ L n = L such that rk R L i = i and all the quotient Lie algebras L i +1 ⁄ L i , i =0,…, n -1, are abelian. We also describe all maximal (with respect to inclusion) locally nilpotent subalgebras L of the Lie algebra R Der K A with rk R L =3. Cite as: Petravchuk A. P., Shevchyk O. M., Sysak K. Ya . Locally nilpotent Lie algebras of deri­vations of integral domains // Appl. Probl. Mech. Math. – 2017. – No. 15. – С. 7–15.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114703082","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
On the classification of rational four-dimensional unital division algebras 有理四维一元除法代数的分类
arXiv: Rings and Algebras Pub Date : 2018-02-23 DOI: 10.4064/cm8021-11-2019
Gustav Hammarhjelm
{"title":"On the classification of rational four-dimensional unital division algebras","authors":"Gustav Hammarhjelm","doi":"10.4064/cm8021-11-2019","DOIUrl":"https://doi.org/10.4064/cm8021-11-2019","url":null,"abstract":"In a paper by E. Dieterich 2017, the category $mathscr{C}(k)$ of four-dimensional unital division algebras, whose right nucleus is non-trivial and whose automorphism group contains Klein's four group $V$, is studied over a general ground field $k$ with $mathrm{char},kneq 2$. In particular, the objects in $mathscr{C}(k)$ are exhaustively constructed from parameters in $k^3$ and explicit isomorphism conditions for the constructed objects are found in terms of these parameters. \u0000In this paper, we specialize to the case $k=mathbb{Q}$ and present results towards a classification of $mathscr{C}(mathbb{Q})$. In particular, for each field $ell$ with $[ell:k]=2$ we present explicity a two-parameter family of pairwise non-isomorphic non-associative objects in $mathscr{C}(mathbb{Q})$ that admit $ell$ as a subfield and we provide a method for classifying the full subcategory of central skew fields admitting $ell$ as a subfield and $kV$-submodule. We also classify the subcategory of $mathscr{C}(mathbb{Q})$ of all four-dimensional Galois extensions of $mathbb{Q}$ with Galois group $V$ that admit $ell$ as a subfield.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115257124","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
The reduced ring order and lower semi-lattices 简化环阶和下半格
arXiv: Rings and Algebras Pub Date : 2018-02-20 DOI: 10.1090/conm/715/14406
W. Burgess, R. Raphael
{"title":"The reduced ring order and lower semi-lattices","authors":"W. Burgess, R. Raphael","doi":"10.1090/conm/715/14406","DOIUrl":"https://doi.org/10.1090/conm/715/14406","url":null,"abstract":"Every reduced ring $R$ has a natural partial order defined by $ale b$ if $a^2=ab$; it generalizes the natural order on a boolean ring. The article examines when $R$ is a lower semi-lattice in this order with examples drawn from weakly Baer rings (pp-rings) and rings of continuous functions. Locally connected spaces and basically disconnected spaces give rings $C(X)$ which are such lower semi-lattices. Liftings of countable orthogonal (in this order) sets over surjective ring homomorphisms are studied.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124431748","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: 3
Tilting Modules and Tilting Torsion Pairs 倾斜模块和倾斜扭转副
arXiv: Rings and Algebras Pub Date : 2018-02-19 DOI: 10.1007/978-3-030-43416-8_18
F. Mattiello, Sergio Pavon, A. Tonolo
{"title":"Tilting Modules and Tilting Torsion Pairs","authors":"F. Mattiello, Sergio Pavon, A. Tonolo","doi":"10.1007/978-3-030-43416-8_18","DOIUrl":"https://doi.org/10.1007/978-3-030-43416-8_18","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121911165","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
The Multiplicative Ideal Theory of Leavitt Path Algebras of Directed Graphs—A Survey 有向图的Leavitt路径代数的乘法理想理论——综述
arXiv: Rings and Algebras Pub Date : 2018-02-19 DOI: 10.1007/978-3-030-43416-8_16
K. Rangaswamy
{"title":"The Multiplicative Ideal Theory of Leavitt Path Algebras of Directed Graphs—A Survey","authors":"K. Rangaswamy","doi":"10.1007/978-3-030-43416-8_16","DOIUrl":"https://doi.org/10.1007/978-3-030-43416-8_16","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122860880","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: 2
On convergence of infinite matrix products with alternating factors from two sets of matrices 关于两组矩阵的交替因子无穷矩阵积的收敛性
arXiv: Rings and Algebras Pub Date : 2017-12-18 DOI: 10.1155/2018/9216760
V. Kozyakin
{"title":"On convergence of infinite matrix products with alternating factors from two sets of matrices","authors":"V. Kozyakin","doi":"10.1155/2018/9216760","DOIUrl":"https://doi.org/10.1155/2018/9216760","url":null,"abstract":"We consider the question of the boundedness of matrix products $A_{n}B_{n}cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}inmathscr{A}$ and $B_{i}inmathscr{B}$, due to an appropriate choice of matrices ${B_{i}}$. It is assumed that for any sequence of matrices ${A_{i}}$ there is a sequence of matrices ${B_{i}}$ for which the sequence of matrix products ${A_{n}B_{n}cdots A_{1}B_{1}}_{n=1}^{infty}$ is norm bounded. Some situations are described in which in this case the norms of matrix products $A_{n}B_{n}cdots A_{1}B_{1}$ are uniformly bounded, that is, $|A_{n}B_{n}cdots A_{1}B_{1}|le C$ for all natural numbers $n$, where $C>0$ is some constant independent of the sequence ${A_{i}}$ and the corresponding sequence ${B_{i}}$. In the general case, the question of the validity of the corresponding statement remains open.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127729885","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: 2
Isomorphisms of graded path algebras 梯度路径代数的同构
arXiv: Rings and Algebras Pub Date : 2017-12-05 DOI: 10.1090/proc/15425
Jason Gaddis
{"title":"Isomorphisms of graded path algebras","authors":"Jason Gaddis","doi":"10.1090/proc/15425","DOIUrl":"https://doi.org/10.1090/proc/15425","url":null,"abstract":"We prove that if two path algebras with homogeneous relations are isomorphic as algebras, then they are isomorphic as graded path algebras. This extends a result by Bell and Zhang in the connected case.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114274256","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: 3
Quantum Observables on a Completely Simple Semigroup 完全简单半群上的量子可观测量
arXiv: Rings and Algebras Pub Date : 2017-11-22 DOI: 10.1142/9789814447546_0006
P. Feinsilver
{"title":"Quantum Observables on a Completely Simple Semigroup","authors":"P. Feinsilver","doi":"10.1142/9789814447546_0006","DOIUrl":"https://doi.org/10.1142/9789814447546_0006","url":null,"abstract":"Completely simple semigroups arise as the support of limiting measures of random walks on semigroups. Such a limiting measure is supported on the kernel of the semigroup. Forming tensor powers of the random walk leads to a hierarchy of the limiting kernels. Tensor squares lead to quantum observables on the kernel. Recall that zeons are bosons modulo the basis elements squaring to zero. Using zeon powers leads naturally to quantum observables which reveal the structure of the kernel. Thus asymptotic information about the random walk is related to algebraic properties of the zeon powers of the random walk.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123040794","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
Self-dual binary quadratic operads 自对偶二元二次操作数
arXiv: Rings and Algebras Pub Date : 2017-11-10 DOI: 10.17377/semi.2017.14.110
P. Kolesnikov
{"title":"Self-dual binary quadratic operads","authors":"P. Kolesnikov","doi":"10.17377/semi.2017.14.110","DOIUrl":"https://doi.org/10.17377/semi.2017.14.110","url":null,"abstract":"We describe those binary quadratic operads generated by a two-dimensional space that are isomorphic to their Koszul dual operads.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132750340","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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