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

Authors : Grigore CALUGAREANU

Pages : 41-45

Doi:10.15672/hujms.622655

View : 12 | Download : 4

Publication Date : 2021-02-04

Article Type : Research Paper

Abstract :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 $\mathbb{Z}$.
Keywords : nil clean, clean, similarity, binary quadratic form, class number