Search results for "Degenerate traces"
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Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…