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Linear functions preserving Green's relations over fieldsстатья
Информация о цитировании статьи получена из
Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 15 сентября 2021 г.
- Авторы: Guterman Alexander, Johnson Marianne, Kambites Mark, Maksaev Artem
- Журнал: Linear Algebra and Its Applications
- Том: 611
- Год издания: 2021
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 310
- Последняя страница: 333
- DOI: 10.1016/j.laa.2020.10.033
- Аннотация: We study linear functions on the space of n×n matrices over a field which preserve or strongly preserve each of Green's equivalence relations (L, R, H and J) and the corresponding pre-orders. For each of these relations we are able to completely describe all preservers over an algebraically closed field (or more generally, a field in which every polynomial of degree n has a root), and all strong preservers and bijective preservers over any field. Over a general field, the non-zero J-preservers are all bijective and coincide with the bijective rank-1 preservers, while the non-zero H-preservers turn out to be exactly the invertibility preservers, which are known. The L- and R-preservers over a field with “few roots” seem harder to describe: we give a family of examples showing that they can be quite wild.
- Добавил в систему: Максаев Артем Максимович