The nil-clean $2\times 2$ integral units

Grigore Calugareanu

doi:10.15672/hujms.622655

Araştırma Makalesi

Yıl 2021, Cilt: 50 Sayı: 1, 41 - 45, 04.02.2021

Grigore Calugareanu

https://doi.org/10.15672/hujms.622655

Öz

Kaynakça

[1] T. Andreescu and D. Andrica, Number Theory. Structures, examples, and problems, Birkhäuser Boston, Inc., Boston, MA, 2009.
[2] A.I. Borevich and I.R. Shafarevich, Number Theory. Pure and Applied Mathematics Vol. 20, Academic Press, New York-London, 1966.
[3] J. Buchmann and U. Vollmer, Binary Quadratic Forms. Springer, Berlin 2007.
[4] A.J. Diesl, Nil clean rings, J. Algebra 383, 197-211, 2013.
[5] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229, 269-278, 1977.
[6] A. Steger, Diagonalibility of Idempotent Matrices. Pacific J. Math. 19 (3), 535-542, 1966.

The nil-clean $2\times 2$ integral units

Yıl 2021, Cilt: 50 Sayı: 1, 41 - 45, 04.02.2021

Grigore Calugareanu

https://doi.org/10.15672/hujms.622655

Öz

We prove that all trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$ are nil-clean and, up to similarity, that there are only two trace $1$, $2\times 2$ invertible matrices over $\mathbb{Z}$.

Anahtar Kelimeler

nil-clean, clean, similarity, binary quadratic form, class number

Kaynakça

[1] T. Andreescu and D. Andrica, Number Theory. Structures, examples, and problems, Birkhäuser Boston, Inc., Boston, MA, 2009.
[2] A.I. Borevich and I.R. Shafarevich, Number Theory. Pure and Applied Mathematics Vol. 20, Academic Press, New York-London, 1966.
[3] J. Buchmann and U. Vollmer, Binary Quadratic Forms. Springer, Berlin 2007.
[4] A.J. Diesl, Nil clean rings, J. Algebra 383, 197-211, 2013.
[5] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229, 269-278, 1977.
[6] A. Steger, Diagonalibility of Idempotent Matrices. Pacific J. Math. 19 (3), 535-542, 1966.

Toplam 6 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Grigore Calugareanu 0000-0002-3353-6958
Yayımlanma Tarihi	4 Şubat 2021
Yayımlandığı Sayı	Yıl 2021 Cilt: 50 Sayı: 1

Kaynak Göster

APA	Calugareanu, G. (2021). The nil-clean $2\times 2$ integral units. Hacettepe Journal of Mathematics and Statistics, 50(1), 41-45. https://doi.org/10.15672/hujms.622655
AMA	Calugareanu G. The nil-clean $2\times 2$ integral units. Hacettepe Journal of Mathematics and Statistics. Şubat 2021;50(1):41-45. doi:10.15672/hujms.622655
Chicago	Calugareanu, Grigore. “The Nil-Clean $2\times 2$ Integral Units”. Hacettepe Journal of Mathematics and Statistics 50, sy. 1 (Şubat 2021): 41-45. https://doi.org/10.15672/hujms.622655.
EndNote	Calugareanu G (01 Şubat 2021) The nil-clean $2\times 2$ integral units. Hacettepe Journal of Mathematics and Statistics 50 1 41–45.
IEEE	G. Calugareanu, “The nil-clean $2\times 2$ integral units”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 1, ss. 41–45, 2021, doi: 10.15672/hujms.622655.
ISNAD	Calugareanu, Grigore. “The Nil-Clean $2\times 2$ Integral Units”. Hacettepe Journal of Mathematics and Statistics 50/1 (Şubat 2021), 41-45. https://doi.org/10.15672/hujms.622655.
JAMA	Calugareanu G. The nil-clean $2\times 2$ integral units. Hacettepe Journal of Mathematics and Statistics. 2021;50:41–45.
MLA	Calugareanu, Grigore. “The Nil-Clean $2\times 2$ Integral Units”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 1, 2021, ss. 41-45, doi:10.15672/hujms.622655.
Vancouver	Calugareanu G. The nil-clean $2\times 2$ integral units. Hacettepe Journal of Mathematics and Statistics. 2021;50(1):41-5.