Research Article
BibTex RIS Cite
Year 2021, , 16 - 65, 17.07.2021
https://doi.org/10.24330/ieja.969577

Abstract

References

  • J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, Julia: a fresh approach to numerical computing, SIAM Review, 59 (2017), 65-98.
  • T. Breuer, SingerAlg, Loewy lengths of certain algebras, Version 1.0.1, (http://www.math.rwth-aachen.de/~Thomas.Breuer/singeralg/), Jan 2021, GAP package.
  • T. Breuer, L. Hethelyi, E. Horvath, and B. Kulshammer, The Loewy structure of certain fixpoint algebras, Part I, J. Algebra, 558 (2020), 199-220.
  • Harold Davenport, Multiplicative Number Theory, Second Edition, Springer-Verlag, New York-Berlin, 1980.
  • The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.11.0, 2020. (https://www.gap-system.org)
  • S. Louboutin, Majoration au point 1 des fonctions L associees aux caracteres de Dirichlet primitifs, ou au caractere d'une extension quadratique d'un corps quadratique imaginaire principal, J. Reine Angew. Math., 419 (1991), 213-219.
  • S. Montgomery, Fixed Rings of Finite Automorphism Groups of Associative Rings, Lecture Notes in Math. 818, Springer-Verlag, Berlin, 1980.
  • J.-P. Serre, A Course in Arithmetic, Springer-Verlag, New York, 1973.
  • C. Small, Sums of powers in large finite fields, Proc. Amer. Math. Soc., 65 (1977), 35-36.
  • I. N. Stewart, Galois Theory, Fourth Edition, CRC Press, Boca Raton, 2015.

THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II

Year 2021, , 16 - 65, 17.07.2021
https://doi.org/10.24330/ieja.969577

Abstract

In Part I of this paper, we introduced a class of certain algebras of finite dimension over a field.
All these algebras are split, symmetric and local. Here we continue to investigate their Loewy structure.
We show that in many cases their Loewy length is equal to an upper bound established in Part I,
but we also construct examples where we have a strict inequality.
The algebras considered here include certain rings of fixpoints
under the action of particular finite groups.
Thus we consider the results in this paper as a contribution to
the general theory of fixpoint rings.

References

  • J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, Julia: a fresh approach to numerical computing, SIAM Review, 59 (2017), 65-98.
  • T. Breuer, SingerAlg, Loewy lengths of certain algebras, Version 1.0.1, (http://www.math.rwth-aachen.de/~Thomas.Breuer/singeralg/), Jan 2021, GAP package.
  • T. Breuer, L. Hethelyi, E. Horvath, and B. Kulshammer, The Loewy structure of certain fixpoint algebras, Part I, J. Algebra, 558 (2020), 199-220.
  • Harold Davenport, Multiplicative Number Theory, Second Edition, Springer-Verlag, New York-Berlin, 1980.
  • The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.11.0, 2020. (https://www.gap-system.org)
  • S. Louboutin, Majoration au point 1 des fonctions L associees aux caracteres de Dirichlet primitifs, ou au caractere d'une extension quadratique d'un corps quadratique imaginaire principal, J. Reine Angew. Math., 419 (1991), 213-219.
  • S. Montgomery, Fixed Rings of Finite Automorphism Groups of Associative Rings, Lecture Notes in Math. 818, Springer-Verlag, Berlin, 1980.
  • J.-P. Serre, A Course in Arithmetic, Springer-Verlag, New York, 1973.
  • C. Small, Sums of powers in large finite fields, Proc. Amer. Math. Soc., 65 (1977), 35-36.
  • I. N. Stewart, Galois Theory, Fourth Edition, CRC Press, Boca Raton, 2015.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

T. Breuer This is me

L. L. Hethelyı This is me

E. Horvath This is me

B. Kulshammer This is me

Publication Date July 17, 2021
Published in Issue Year 2021

Cite

APA Breuer, T., L. Hethelyı, L., Horvath, E., Kulshammer, B. (2021). THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II. International Electronic Journal of Algebra, 30(30), 16-65. https://doi.org/10.24330/ieja.969577
AMA Breuer T, L. Hethelyı L, Horvath E, Kulshammer B. THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II. IEJA. July 2021;30(30):16-65. doi:10.24330/ieja.969577
Chicago Breuer, T., L. L. Hethelyı, E. Horvath, and B. Kulshammer. “THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II”. International Electronic Journal of Algebra 30, no. 30 (July 2021): 16-65. https://doi.org/10.24330/ieja.969577.
EndNote Breuer T, L. Hethelyı L, Horvath E, Kulshammer B (July 1, 2021) THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II. International Electronic Journal of Algebra 30 30 16–65.
IEEE T. Breuer, L. L. Hethelyı, E. Horvath, and B. Kulshammer, “THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II”, IEJA, vol. 30, no. 30, pp. 16–65, 2021, doi: 10.24330/ieja.969577.
ISNAD Breuer, T. et al. “THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II”. International Electronic Journal of Algebra 30/30 (July 2021), 16-65. https://doi.org/10.24330/ieja.969577.
JAMA Breuer T, L. Hethelyı L, Horvath E, Kulshammer B. THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II. IEJA. 2021;30:16–65.
MLA Breuer, T. et al. “THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II”. International Electronic Journal of Algebra, vol. 30, no. 30, 2021, pp. 16-65, doi:10.24330/ieja.969577.
Vancouver Breuer T, L. Hethelyı L, Horvath E, Kulshammer B. THE LOEWY STRUCTURE OF CERTAIN FIXPOINT ALGEBRAS, PART II. IEJA. 2021;30(30):16-65.