On sum of a nilpotent and an ideally finite algebras

• Date: 2018
• Main Author: Bilun, Svitlana V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: associative algebra; field; sum of subalgebras; finite dimensional ideal; left annihilator; 16N40
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/856
• Journal Title: Algebra and Discrete Mathematics

We study associative algebras \(R\) over  arbitrary fields which can be decomposed into a sum \(R=A+B\) of their subalgebras \(A\) and \(B\) such that \(A^{2}=0\) and \(B\) is ideally finite (is a sum of its finite dimensional ideals). We prove that \(R\) has a locally nilpotent ideal \(I\) such tha...