Urban, E. On residually reducible representations on local rings. (English) Zbl 0996.16007 J. Algebra 212, No. 2, 738-742 (1999). Let \(A\) be a local Artinian ring with maximal ideal \(\mathcal M\), let \(R\) be an \(A\)-algebra and let \(\rho\) be an \(A\)-representation of \(R\). If the residual representation \(\overline\rho\) (that is, with values in the residue field) is absolutely irreducible, then it is well-known by a result of Carayol that \(\rho\) is completely determined by its trace. This is no longer true in the reducible case. The author proves a version of this result assuming some further hypothesis. Reviewer: F.U.Coelho (São Paulo) Cited in 1 ReviewCited in 12 Documents MSC: 16G10 Representations of associative Artinian rings 16P20 Artinian rings and modules (associative rings and algebras) Keywords:reducible representations; local Artinian rings; traces PDFBibTeX XMLCite \textit{E. Urban}, J. Algebra 212, No. 2, 738--742 (1999; Zbl 0996.16007) Full Text: DOI References: [1] Carayol, H., Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet, Contemp. Math., 165, 213-235 (1994) · Zbl 0812.11036 [2] E. Urban, Selmer groups and the Eisenstein-Klingen ideal, Oct. 1997; E. Urban, Selmer groups and the Eisenstein-Klingen ideal, Oct. 1997 · Zbl 1061.11027 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.