On \(0\)-semisimplicity of linear hulls of generators for semigroups generated by idempotents

• Date: 2018
• Main Authors: Bondarenko, Vitaliy M., Tertychna, Olena M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: semigroup; matrix representations; defining relations; \(0\)-semisimple matrix; 16G; 20M30
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/718
• Journal Title: Algebra and Discrete Mathematics

Let \(I\) be a finite set (without \(0\)) and \(J\) a subset of \(I\times I\)  without diagonal elements. Let \(S(I,J)\) denotes the semigroup generated by \(e_0=0\) and \(e_i\), \(i\in I\), with the following  relations: \(e_i^2=e_i\) for any \(i\in I\), \(e_ie_j=0\) for any  \((i,j)\in J\). In thi...