2019
Том 71
№ 4

All Issues

Słowik R.

Articles: 2
Article (English)

The Drazin inverses of infinite triangular matrices and their linear preservers

Słowik R.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 4. - pp. 534-548

We consider the ring of all infinite $(N \times N)$ upper triangular matrices over a field $F$. We give a description of elements that are Drazin invertible in this ring. In the case where $F$ is such that $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(F) \not = 2$ and $| F| > 4$, we find the form of linear preservers for the Drazin inverses.

Brief Communications (English)

Expressing infinite matrices as sums of idempotents

Słowik R.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 8. - pp. 1145-1147

Let $\scr M_{Cf} (F)$ be the set of all column-finite $N \times N$ matrices over a field $F$. The following problem is studied: what elements of $\scr M_{Cf} (F)$ can be expressed as a sum of idempotents? The result states that every element of $\scr M_{Cf} (F)$ can be represented as the sum of 14 idempotents.