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## Automorphisms of a certain subalgebra of the upper triangular matrix algebra

#### Özkay ÖZKAN [1] , Mustafa AKKURT [2]

For a commutative ring $R$ with unity, the $R$-algebra of strictly upper triangular $n\times n$ matrices over $R$ is denoted by $N_{n}\left( R\right)$, where $n$ is a positive integer greater than $1$. For the identity matrix $I$, $\alpha \in R$, $A \in N_n(R)$, the set of all elements $\alpha I+A$ is defined as the scalar upper triangular matrix algebra $ST_n(R)$ which is a subalgebra of the upper triangular matrices $T_n(R) .$ In this paper, we investigate the $R$-algebra automorphisms of $ST_{n}\left( R\right) .$ We extend the automorphisms of $N_{n}\left( R\right)$ to $ST_{n}\left( R\right)$ and classify all the automorphisms of $ST_{n}\left( R\right) .$ We generalize the results of Cao and Wang and prove that not all automorphisms of $ST_{n}\left( R\right)$ can be extended to the automorphisms of $T_{n}(R).$
triangular matrix algebra, upper triangular matrix algebra, automorphisms
• [1] Y. Cao and J. Wang, A note on algebra automorphisms of strictly upper triangular matrices over commutative rings, Linear Algebra Appl. 311, 187–193, 2000.
• [2] S.P. Coelho, Automorphism group of certain algebras of triangular matrices, Arch. Math. 61, 119–123, 1993.
• [3] T.P. Kezlan, A note on algebra automorphisms of triangular matrices over commutative rings, Linear Algebra Appl. 135, 181–184, 1990.
Primary Language en Mathematics Mathematics Orcid: 0000-0001-6755-1497Author: Özkay ÖZKAN (Primary Author)Institution: GEBZE TECHNICAL UNIVERSITYCountry: Turkey Orcid: 0000-0002-8072-8426Author: Mustafa AKKURT Institution: GEBZE TECHNICAL UNIVERSITYCountry: Turkey Publication Date : June 2, 2020
 Bibtex @research article { hujms513851, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1150 - 1158}, doi = {10.15672/hujms.513851}, title = {Automorphisms of a certain subalgebra of the upper triangular matrix algebra}, key = {cite}, author = {Özkan, Özkay and Akkurt, Mustafa} } APA Özkan, Ö , Akkurt, M . (2020). Automorphisms of a certain subalgebra of the upper triangular matrix algebra . Hacettepe Journal of Mathematics and Statistics , 49 (3) , 1150-1158 . DOI: 10.15672/hujms.513851 MLA Özkan, Ö , Akkurt, M . "Automorphisms of a certain subalgebra of the upper triangular matrix algebra" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1150-1158 Chicago Özkan, Ö , Akkurt, M . "Automorphisms of a certain subalgebra of the upper triangular matrix algebra". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1150-1158 RIS TY - JOUR T1 - Automorphisms of a certain subalgebra of the upper triangular matrix algebra AU - Özkay Özkan , Mustafa Akkurt Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.513851 DO - 10.15672/hujms.513851 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1150 EP - 1158 VL - 49 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.513851 UR - https://doi.org/10.15672/hujms.513851 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Automorphisms of a certain subalgebra of the upper triangular matrix algebra %A Özkay Özkan , Mustafa Akkurt %T Automorphisms of a certain subalgebra of the upper triangular matrix algebra %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 3 %R doi: 10.15672/hujms.513851 %U 10.15672/hujms.513851 ISNAD Özkan, Özkay , Akkurt, Mustafa . "Automorphisms of a certain subalgebra of the upper triangular matrix algebra". Hacettepe Journal of Mathematics and Statistics 49 / 3 (June 2020): 1150-1158 . https://doi.org/10.15672/hujms.513851 AMA Özkan Ö , Akkurt M . Automorphisms of a certain subalgebra of the upper triangular matrix algebra. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 1150-1158. Vancouver Özkan Ö , Akkurt M . Automorphisms of a certain subalgebra of the upper triangular matrix algebra. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 1150-1158.

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