A ring $R$ is Zhou nil-clean if every element in $R$ is the sum of a nilpotent and two tripotents. Let $R$ be a Zhou nil-clean ring. If $R$ is of bounded index or 2-primal, we prove that every square matrix over $R$ is the sum of a nilpotent and a linear combination of two idempotents. This provides a large class of rings over which every square matrix has such decompositions by nilpotent and linear combination of idempotent matrices. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
Idempotent matrix nilpotent matrix linear combination Zhou nil-clean ring
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 14 Temmuz 2020 |
Yayımlandığı Sayı | Yıl 2020 |