Öz
Kaynakça
- 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.
Öz
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.
Anahtar Kelimeler
Fixpoint algebra symmetric algebra Jacobson radical Loewy length
Kaynakça
- 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 17 Temmuz 2021 |
| Yayımlandığı Sayı | Yıl 2021 |