We (completely) determine those natural numbers n for which the full matrix ring \(\mathbb{M}_n(\mathbb{F}_2)\) and the triangular matrix ring \(\mathbb{T}_n(\mathbb{F}_2)\) over the two elements field \(\mathbb{F}_2\) 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 \(\mathbb{M}_n(\mathbb{F}_2)\) for all naturals \(n\geq 1\), established in Linear Algebra & Appl. (2013) by Breaz–Călugăreanu–Danchev–Micu and again in Linear Algebra & Appl. (2018) by Šter as well as in Indag. Math. (2019) by Shitov.

我们（完全）确定自然矩阵n的全矩阵环\（\ mathbb {M} _n（\ mathbb {F} _2）\）和三角形矩阵环\（\ mathbb {T} _n（\ mathbb { F} _2）\）在两个元件字段\（\ mathbb {F} _2 \）要么ñ -torsion清洁或几乎ñ分别-torsion干净。这些结果多少可以解决并解决一个问题，这是Danchev–Matczuk最近在当代杂志上提出的。数学。（2019），以及它们以更精确的方式提供完整的矩阵的零-清洁性能\（N \ n次\）环\（\ mathbb {M} \ mathbb {F} _2）\ _n（）为所有自然\（n \ geq 1 \），建立于Linear Algebra＆Appl。（2013）由Breaz–Călugăreanu–Danchev–Micu撰写，并再次发表于Linear Algebra＆Appl。（2018）由Šter以及Indag撰写。数学。Shitov（2019）。