On some special generalized functional identities.
A theorem by \textit{M. A. Chebotar} [J. Algebra 202, No. 2, 655-670 (1998; Zbl 0907.16008)] shows that the existence of a non-standard solution of a generalized functional identity (GFI) on a prime ring \(R\) implies that \(R\) is a GPI ring. The paper under review studies some special GFI's on \(R\) for which a more refined conclusion can be derived. More precisely, the following types of GFI's are considered: (i) GFI's that have only standard solutions in any case, i.e. regardless of whether \(R\) is GPI or not, (ii) GFI's for which the existence of a non-standard solution yields that their coefficients lie in the socle of the central closure, and (iii) GFI's for which the existence of a non-standard solution yields some information about the structure of the associated division algebra of the central closure of \(R\).
scientific article; zbMATH DE number 2113502