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Research Article

On the lengths of matrix incidence algebras with radicals of square zero

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Pages 1736-1753 | Received 02 Jul 2021, Accepted 22 Mar 2022, Published online: 12 May 2022

References

  • Paz A. An application of the Cayley-Hamilton theorem to matrix polynomials in several variables. Linear Multilinear Algebra. 1984;15:161–170.
  • Guterman A, Laffey T, Markova O, et al. A resolution of Paz's conjecture in the presence of a nonderogatory matrix. Linear Algebra Appl. 2018;543:234–250.
  • Longstaff WE. Irreducible families of complex matrices containing a rank-one matrix. Bull Aust Math Soc. 2020;102(2):226–236.
  • Shitov Y. An improved bound for the lengths of matrix algebras. Algebra Number Theory. 2019;13(6):1501–1507.
  • Guterman AE, Kudryavtsev DK. Characteristic sequences of non-associative algebras. Commun Algebra. 2020;48:1713–1725.
  • Guterman AE, Kudryavtsev DK. Length function and characteristic sequences of quadratic algebras. J Algebra. 2021;579:428–455.
  • Guterman AE, Khrystik M, Markova OV. On the lengths of group algebras of finite abelian groups in the semi-simple case. J Algebra Appl. 2022;2250140.
  • Guterman AE, Khrystik M, Markova OV. On the lengths of group algebras of finite abelian groups in the modular case. J Algebra Appl. 2022;2250117.
  • Brusamarello R, Fornaroli EZ, Santulo Jr EA. Multiplicative automorphisms of incidence algebras. Comm Algebra. 2014;43(2):726–736.
  • Brusamarello R, Lewis DW. Automorphisms and involutions on incidence algebras. Linear Multilinear Algebra. 2011;59(11):1247–1267.
  • Chen RXF, Reidys CM. Linear sequential dynamical systems, incidence algebras, and Möbius functions. Linear Algebra Appl. 2018;553:270–291.
  • Santulo Jr EA, Souza JP, Yasumura FY. Group gradings on finite dimensional incidence algebras. J Algebra. 2020;544:302–328.
  • Kolegov NA. On real algebras generated by positive and nonnegative matrices. Linear Algebra Appl. 2021;611:46–65.
  • Kolegov NA, Markova OV. Systems of generators of matrix incidence algebras over finite fields. J Math Sci, New York. 2019;240:783–798.
  • Longstaff WE, Rosenthal P. Generators of matrix incidence algebras. Australas J Combin. 2000;22:117–121.
  • Markova OV. Length computation of matrix subalgebras of special type. J Math Sci, New York. 2008;155:908–931.
  • Guterman AE, Markova OV, Mehrmann V. Length realizability for pairs of quasi-commuting matrices. Linear Algebra Appl. 2019;568:135–154.
  • Guterman AE, Markova OV. Commutative matrix subalgebras and length function. Linear Algebra Appl. 2009;430:1790–1805.
  • Markova OV. On some properties of the length function. Math Notes. 2010;87:71–78.
  • Markova OV. Upper bound for the length of commutative algebras. Sb Math. 2009;200(12): 1767–1787.
  • Cigler G, Jerman M, Wojciechowski PJ. Full algebras of matrices. Linear Multilinear Algebra. 2019;67(8):1511–1521.
  • Spiegel E, O'Donnell CJ. Incidence algebras. New York (NY): Marcel Dekker, Inc.; 1997.
  • Mirzakhani M. A simple proof of a theorem of Schur. Am Math Mon. 1998;105(3):260–262.
  • Markov VT. personal communication. [cited 2018 Oct 22].

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