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- W4381491490 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]." @default.
- W4381491490 created "2023-06-22" @default.
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- W4381491490 date "2023-09-20" @default.
- W4381491490 modified "2023-10-14" @default.
- W4381491490 title "Gradings on block-triangular matrix algebras" @default.
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- W4381491490 doi "https://doi.org/10.1090/proc/16586" @default.
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