n-Torsion Clean and Almost n-Torsion Clean Matrix Rings
Copyright policy )n-Torsion Clean and Almost n-Torsion Clean Matrix Rings
We completely determine those natural numbers $n$ for which the full matrix ring $M_n(F_2)$ and the triangular matrix ring $T_n(F_2)$ over the two elements field $F_2$ are either n-torsion clean or are almost n-torsion clean, respectively. These results somewhat address and settle a question, recently posed by Danchev-Matczuk in Contemp. Math. (2019) as well as they supply in a more precise aspect the nil-cleanness property of the full matrix $n\times n$ ring $M_n(F_2)$ for all naturals $n \geq 1$, established in Linear Algebra and Appl. (2013) by Breaz-Calugareanu-Danchev-Micu and again in Linear Algebra & Appl. (2018) by Ster as well as in Indag. Math. (2020) by Shitov.
15 pages
- Institute of Mathematics and Informatics Bulgaria
- Bulgarian Academy of Sciences Bulgaria
- Babeș-Bolyai University Romania
Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, 16U99, 16E50, 13B99
Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, 16U99, 16E50, 13B99
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