Year: 2026
Type: article
Abstract: We present matrices as graded regular BiHom-associative algebras and study several features of their decompositions. More precisely, we introduce a notion of connection in the support of the grading and use it to construct a family of canonical graded ideals. We show that, under suitable assumptions, including Σ-multiplicativity, maximal length and triviality of the centre, the matrix regular BiHom-associative algebra decomposes into a direct sum of graded simple ideals. We further extend our results to general graded regular BiHom-associative algebras over arbitrary base fields. As applications, we reinterpret classical gradings on matrix algebras such as those induced by Pauli matrices and the ℤn × ℤn-grading in terms of our setting.
Source: Quaestiones Mathematicae
Authors: Jiacheng Sun, Shuanhong Wang, Haoran Zhu
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1289679015
OpenAlex ID: W4415030933
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