Exponent matrices and Frobenius rings

• Date: 2018
• Main Authors: Dokuchaev, M. A., Kasyanuk, M. V., Khibina, M. A., Kirichenko, V. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: exponent matrix; Frobenius ring; distributive module; quiver of semiperfect ring; 16P40; 16P20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1056
• Journal Title: Algebra and Discrete Mathematics

We give a survey of results connecting the exponent matrices with Frobenius rings. In particular, we prove that for any parmutation \(\sigma \in S_{n}\) there exists a countable set of indecomposable Frobenius semidistributive rings \(A_{m}\) with Nakayama permutation \( \sigma\).