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Relevant bibliographies by topics / Ring of upper triangular matrices

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Academic literature on the topic 'Ring of upper triangular matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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Journal articles on the topic "Ring of upper triangular matrices"

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Słowik, Roksana, and Driss Aiat Hadj Ahmed. "m-commuting maps on triangular and strictly triangular infinite matrices." Electronic Journal of Linear Algebra 37 (March 24, 2021): 247–55. http://dx.doi.org/10.13001/ela.2021.5083.

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Let $N_\infty(F)$ be the ring of infinite strictly upper triangular matrices with entries in an infinite field. The description of the commuting maps defined on $N_\infty(F)$, i.e. the maps $f\colon N_\infty(F)\rightarrow N_\infty(F)$ such that $[f(X),X]=0$ for every $X\in N_\infty(F)$, is presented. With the use of this result, the form of $m$-commuting maps defined on $T_\infty(F)$ -- the ring of infinite upper triangular matrices, i.e. the maps $f\colon T_\infty(F)\rightarrow T_\infty(F)$ such that $[f(X),X^m]=0$ for every $X\in T_\infty(F)$, is found.

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Benkovič, Dominik. "Lie Triple Derivations on Triangular Matrices." Algebra Colloquium 18, spec01 (2011): 819–26. http://dx.doi.org/10.1142/s1005386711000708.

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Let [Formula: see text] be the algebra of all n × n upper triangular matrices over a commutative unital ring [Formula: see text], and let [Formula: see text] be a 2-torsion free unital [Formula: see text]-bimodule. We show that every Lie triple derivation [Formula: see text] is a sum of a standard Lie derivation and an antiderivation.

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Bounds, Jordan. "Commuting maps over the ring of strictly upper triangular matrices." Linear Algebra and its Applications 507 (October 2016): 132–36. http://dx.doi.org/10.1016/j.laa.2016.05.041.

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Wang, Long, Xianwen Fang, and Fenglei Tian. "Automorphisms of the total graph over upper triangular matrices." Journal of Algebra and Its Applications 19, no. 08 (2019): 2050161. http://dx.doi.org/10.1142/s0219498820501613.

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Let [Formula: see text] be a finite field, [Formula: see text] the ring of all [Formula: see text] upper triangular matrices over [Formula: see text], [Formula: see text] the set of all zero-divisors of [Formula: see text], i.e. [Formula: see text] consists of all [Formula: see text] upper triangular singular matrices over [Formula: see text]. The total graph of [Formula: see text], denoted by [Formula: see text], is a graph with all elements of [Formula: see text] as vertices, and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we dete

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Huang, Juan, Hailan Jin, Tai Keun Kwak, Yang Lee, and Zhelin Piao. "Remarks on Centers of Rings." Algebra Colloquium 28, no. 01 (2021): 1–12. http://dx.doi.org/10.1142/s100538672100002x.

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It is proved that for matrices [Formula: see text], [Formula: see text] in the [Formula: see text] by [Formula: see text] upper triangular matrix ring [Formula: see text] over a domain [Formula: see text], if [Formula: see text] is nonzero and central in [Formula: see text] then [Formula: see text]. The [Formula: see text] by [Formula: see text] full matrix rings over right Noetherian domains are also shown to have this property. In this article we treat a ring property that is a generalization of this result, and a ring with such a property is said to be weakly reversible-over-center. The cla

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Nakamoto, Kazunori. "The moduli of representations with Borel mold." International Journal of Mathematics 25, no. 07 (2014): 1450067. http://dx.doi.org/10.1142/s0129167x14500670.

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The author constructs the moduli of representations whose images generate the subalgebra of upper triangular matrices (up to inner automorphisms) of the full matrix ring for any groups and any monoids.

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Yang, Shizhou, Xuemei Song, and Zhongkui Liu. "Power-serieswise McCoy Rings." Algebra Colloquium 18, no. 02 (2011): 301–10. http://dx.doi.org/10.1142/s1005386711000198.

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In this paper, we introduce power-serieswise McCoy rings, which are a generalization of power-serieswise Armendariz rings, and investigate their properties. We show that a ring R is power-serieswise McCoy if and only if the ring consisting of n × n upper triangular matrices with equal diagonal entries over R is power-serieswise McCoy. We also prove that a direct product of rings is power-serieswise McCoy if and only if each of its factors is power-serieswise McCoy. Meanwhile we show that power-serieswise McCoy rings may be neither semi-commutative nor power-serieswise Armendariz.

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Thiem, Nathaniel. "Branching rules in the ring of superclass functions of unipotent upper-triangular matrices." Journal of Algebraic Combinatorics 31, no. 2 (2009): 267–98. http://dx.doi.org/10.1007/s10801-009-0186-z.

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Cao, You'an. "Automorphisms of Certain Lie Algebras of Upper Triangular Matrices over a Commutative Ring." Journal of Algebra 189, no. 2 (1997): 506–13. http://dx.doi.org/10.1006/jabr.1996.6866.

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Cao, Chongguang, and Zhang Xian. "Multiplicative semigroup automorphisms of upper triangular matrices over rings." Linear Algebra and its Applications 278, no. 1-3 (1998): 85–90. http://dx.doi.org/10.1016/s0024-3795(98)10026-5.

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Dissertations / Theses on the topic "Ring of upper triangular matrices"

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Levy, Louis Agnew. "Multipliers for the Lower Central Series of Strictly Upper Triangular Matrices." NCSU, 2008. http://www.lib.ncsu.edu/theses/available/etd-11122008-190848/.

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Lie algebra multipliers and their properties is a recent area of study. A multiplier is the Lie algebra analogue of the Schur multiplier from group theory. By definition a multiplier is central, so we only need to find its dimension in order to characterize it. We will investigate how to find the dimensions of the multipliers for the lower central series of strictly upper triangular matrices. The closed form result is a set of six polynomial answers in two variables: the size of the matrix and the position in the series.

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Bounds, Jordan C. "ON COMMUTING MAPS OVER THE ALGEBRA OF STRICTLY UPPER TRIANGULAR MATRICES." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1462309150.

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Stanley, Laura. "Upper triangular matrices and operations in odd primary connective K-theory." Thesis, University of Sheffield, 2011. http://etheses.whiterose.ac.uk/2015/.

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Let $U_\infty\Z_p$ be the group of infinite invertible upper triangular matrices with entries in the $p$-adic integers. Also let $\Aut_{\text{left-}\ell\text{-mod}}^0(\ell\wedge\ell)$ be the group of left $\ell$-module automorphisms of $\ell\wedge\ell$ which induce the identity on mod $p$ homology, where $\ell$ is the Adams summand of the $p$-adically complete connective $K$-Theory spectrum. In this thesis we construct and prove there is an isomorphism between these two groups. We will then determine a specific matrix (up to conjugacy) which corresponds to the automorphism $1\wedge\psi^q$ of $

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Taylor, Matthew. "On upper triangular tropical matrix semigroups, tropical matrix identities and T-modules." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/on-upper-triangular-tropical-matrix-semigroups-tropical-matrix-identities-and-tmodules(d470a4a1-4eca-46c8-b9b8-4377affcc6fe).html.

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Gonçalves, Dimas José. "A-identidades polinomiais em algebras associativas." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306369.

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Orientador: Plamen Emilov Koshlukov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-12T22:59:30Z (GMT). No. of bitstreams: 1 Goncalves_DimasJose_D.pdf: 561175 bytes, checksum: 463bf9f78a417a27d1bcf83549bc65a9 (MD5) Previous issue date: 2009<br>Resumo: Nesta tese estudamos identidades polinomiais em álgebras associativas. Mais precisamente, estudamos as A-identidades satisfeitas por algumas classes importantes de álgebras. O primeiro resultado principal da tese consiste em uma descriçã

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Wu, Shin-che, and 吳欣哲. "The numerical range of certain nilpotent upper-triangular Toeplitz matrices." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/4wu287.

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碩士<br>東吳大學<br>數學系<br>96<br>Let A be an n-by-n complex matrix. The numerical range of A is theset W(A) = {x*Ax : x belongs to Cn, x*x = 1}. We deal with the circularityproperty of the numerical range of certain nilpotent upper triangularToeplitz matrices. If A is the nilpotent upper triangular Toeplitz matrix of the forms A(a1,a2,0)belongs to M4 or A(a1,a2,0,0)belongs to M5, we provethat W(A) is a circular disk centered at the origin if and only if a1a2=0.Similarly, if A is the nilpotent upper triangular Toeplitz matrix of theforms A(a1,0,a3)belongs to M4 or A(a1,0,a3,0)belongs to M5, W(A) is a

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Nadareishvili, George. "A classification of localizing subcategories by relative homological algebra." Doctoral thesis, 2015. http://hdl.handle.net/11858/00-1735-0000-0028-867A-A.

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Book chapters on the topic "Ring of upper triangular matrices"

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Bart, H., and G. Ph A. Thijsse. "Complementary Triangular Forms of Upper Triangular Toeplitz Matrices." In The Gohberg Anniversary Collection. Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-9144-8_3.

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Bart, H., and G. Ph A. Thijsse. "Complementary Triangular Forms of Upper Triangular Toeplitz Matrices." In The Gohberg Anniversary Collection. Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-9276-6_5.

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Álvarez, Rafael, Francisco Martínez, José-Francisco Vicent, and Antonio Zamora. "Cryptographic Applications of 3x3 Block Upper Triangular Matrices." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28931-6_10.

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Samoilenko, Y. S. "Representations of the Group of Upper Triangular Matrices." In Spectral Theory of Families of Self-Adjoint Operators. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3806-2_8.

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Bart, Harm, Torsten Ehrhardt, and Bernd Silbermann. "Echelon Type Canonical Forms in Upper Triangular Matrix Algebras." In Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49182-0_8.

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Álvarez, Rafael, Joan-Josep Climent, Leandro Tortosa, and Antonio Zamora. "A Pseudorandom Bit Generator Based on Block Upper Triangular Matrices." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-45068-8_57.

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Álvarez, Rafael, Leandro Tortosa, José Vicent, and Antonio Zamora. "A Non-abelian Group Based on Block Upper Triangular Matrices with Cryptographic Applications." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02181-7_13.

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Di Vincenzo, Onofrio, Plamen Koshlukov, and Angela Valenti. "Gradings and graded identities for the upper triangular matrices over an infinite field." In Groups, Rings and Group Rings. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420010961.ch9.

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Aschenbrenner, Matthias, Lou van den Dries, and Joris van der Hoeven. "Triangular Automorphisms." In Asymptotic Differential Algebra and Model Theory of Transseries. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175423.003.0013.

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This chapter focuses on triangular automorphisms, which can be analyzed by Lie techniques. Throughout the discussion K is a commutative ring containing ℚ as a subring. A formalism is introduced to analyze triangular automorphisms of such a polynomial algebra by means of their logarithms, the triangular derivations. After presenting some definitions and simple facts about filtered modules, filtered algebras, and graded algebras, the chapter considers triangular linear maps and the Lie algebra of an algebraic unitriangular group. It then describes derivations on the ring of column-finite matrices, along with iteration matrices and Riordan matrices. It also explains derivations on polynomial rings and concludes by applying triangular automorphisms to differential polynomials.

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Fallat, Shaun M., and Charles R. Johnson. "Bidiagonal Factorization." In Totally Nonnegative Matrices. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691121574.003.0003.

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This chapter introduces and methodically develops the important and useful topic of bidiagonal factorization. Factorization of matrices is one of the most important topics in matrix theory, and plays a central role in many related applied areas such as numerical analysis and statistics. Investigating when a class of matrices admits a particular type of factorization is an important study, which historically has been fruitful. Often many intrinsic properties of a particular class of matrices can be deduced via certain factorization results. For example, it is a well-known fact that any (invertible) M-matrix can be factored into a product of a lower triangular (invertible) M-matrix and an upper triangular (invertible) M-matrix. This LU factorization result leads to the conclusion that the class of M-matrices is closed under Schur complementation, because of the connection between LU factorizations and Schur complements. This chapter focuses on triangular factorization extended beyond just LU factorization, however.

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Conference papers on the topic "Ring of upper triangular matrices"

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Ceballos, Manuel, Juan Núñez, Ángel F. Tenorio, George Maroulis, and Theodore E. Simos. "An Algorithm to Compute Abelian Subalgebras in Linear Algebras of Upper-Triangular Matrices." In COMPUTATIONAL METHODS IN SCIENCE AND ENGINEERING: Advances in Computational Science: Lectures presented at the International Conference on Computational Methods in Sciences and Engineering 2008 (ICCMSE 2008). AIP, 2009. http://dx.doi.org/10.1063/1.3225370.

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Lee, W. C., and F. Ma. "On Simultaneous Triangularization of the Coefficients of Linear Systems." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/cie-1626.

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Abstract The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. An efficient way for the analysis of a nonconservative system is to reduce its coefficient matrices simultaneously to upper triangular forms. The purpose of this paper is to present some criteria for simultaneous triangularization and, when applicable, to expound a constructive procedure for triangularization.

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Choo, Yung K., Woo-Yung Soh, and Seokkwan Yoon. "Application of a Lower-Upper Implicit Scheme and an Interactive Grid Generation for Turbomachinery Flow Field Simulations." In ASME 1989 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/89-gt-20.

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A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a turbine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and

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