Automorphisms of a certain subalgebra of the upper triangular matrix algebra

Özkay ÖZKAN; Mustafa AKKURT

doi:https://doi.org/10.15672/hujms.513851

Makale detayları

Automorphisms of a certain subalgebra of the upper triangular matrix algebra

Yazarlar:

Özkay ÖZKAN | Mustafa AKKURT

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 3, pp.1150-1158

Belge Tipi:

Makale

Yayın Tarihi:

6/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000451104

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.513851

Özet:

 

For a commutative ring RRR with unity, the RRR-algebra of strictly upper triangular n×nn×nn\times n matrices over RRR is denoted by Nn(R)Nn(R)N_{n}\left( R\right) , where nnn is a positive integer greater than 111. For the identity matrix III, α∈Rα∈R\alpha \in R, A∈Nn(R)A∈Nn(R)A \in N_n(R), the set of all elements αI+AαI+A\alpha I+A is defined as the scalar upper triangular matrix algebra STn(R)STn(R)ST_n(R) which is a subalgebra of the upper triangular matrices Tn(R).Tn(R).T_n(R) . In this paper, we investigate the RRR-algebra automorphisms of STn(R).STn(R).ST_{n}\left( R\right) . We extend the automorphisms of Nn(R)Nn(R)N_{n}\left( R\right)  to STn(R)STn(R)ST_{n}\left( R\right) and classify all the automorphisms of STn(R).STn(R).ST_{n}\left( R\right) . We generalize the results of Cao and Wang and prove that not all automorphisms of STn(R)STn(R)ST_{n}\left( R\right)  can be extended to the automorphisms of Tn(R).Tn(R).T_{n}(R).

Makale detayları

Automorphisms of a certain subalgebra of the upper triangular matrix algebra

Yazarlar: Özkay ÖZKAN | Mustafa AKKURT

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 3, pp.1150-1158

Belge Tipi: Makale

Yayın Tarihi: 6/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000451104

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.513851

Sayı

Yazarlar:

Özkay ÖZKAN | Mustafa AKKURT

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 3, pp.1150-1158

Belge Tipi:

Makale

Yayın Tarihi:

6/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000451104

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.513851