| Full text | |
| Author(s): |
Diniz, Diogo
;
Da Silva, Jose Lucas Galdino
;
Koshlukov, Plamen
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. N/A, p. 9-pg., 2023-09-20. |
| Abstract | |
Upper triangular, and more generally, block-triangular matrices, are rather important in Linear Algebra, and also in Ring theory, namely in the theory of PI algebras (algebras that satisfy polynomial identities). The group gradings on such algebras have been extensively studied during the last decades. In this paper we prove that for any group grading on a block-triangular matrix algebra, over an arbitrary field, the Jacobson radical is a graded (homogeneous) ideal. As noted by F. Yasumura [Arch. Math. (Basel) 110 (2018), pp. 327-332] this yields the classification of the group gradings on these algebras and confirms a conjecture made by A. Valenti and M. Zaicev [Arch. Math. (Basel) 89 (2007), pp. 33-40]. (AU) | |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |