\(*\)-differential identities of semiprime rings with involution
Various results in the literature show that differential identities of a ring \(R\) arise from generalized polynomial identities of \(R\), when \(R\) is a semiprime ring, or is a prime ring with involution. The author extends these results to identities of semiprime rings with involution. Let \(R\) be a semiprime ring with involution * and with characteristic \(\neq 2\). If \(\{\Delta_j\}\) are certain ``reduced'' words in the derivations of \(R\), and if \(f(x_i^{\Delta_j},(x_i^{\Delta_j})^*)\) is a *-differential identity for \(R\), the author proves that \(R\) satisfies the *-generalized identity \(f(z_{ij}e(\Delta_j),(z_{ij}e(\Delta_j))^*)\), where \(e(\Delta_j)\) are idempotents in the extended centroid of \(R\), and \(\{z_{ij}\}\) are indeterminates. The proof uses the notion of orthogonal completeness.
scientific article; zbMATH DE number 954752