D’Este, Gabriella Nonadmissible genealogical trees. (English) Zbl 0741.05022 Rend. Semin. Mat. Univ. Padova 79, 71-86 (1988). The author continues her study of admisible words initiated in a previous paper [same journal 75, 247-251 (1986; Zbl 0602.16026)]. Admissiblity of a word is defined in terms of admissibility of an oriented tree, called a genealogical tree. The author obtains a criterion for the nonadmissibility of a genealogical tree, and uses it to determine a class of nonadmissible words. These results are applied to investigate the structure of a module constructed over a particularly simple genealogical tree which is shown to provide an example of an injective cogenerator for the category of all \(K[x]\)-modules (where \(K[x]\) denotes the polynomial algebra over a field \(K\)). MSC: 05C05 Trees 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:admisible words; genealogical tree Citations:Zbl 0602.16026 PDFBibTeX XMLCite \textit{G. D'Este}, Rend. Semin. Mat. Univ. Padova 79, 71--86 (1988; Zbl 0741.05022) Full Text: Numdam EuDML References: [1] G. D’Este , Extended strings and admissible words , Rend. Sem. Mat. Univ. Padova , 75 ( 1986 ), pp. 247 - 251 . Numdam | MR 847669 | Zbl 0602.16026 · Zbl 0602.16026 [2] C.M. Ringel , The indecomposable representations of the dihedral 2-groups , Math. Ann. , 214 ( 1975 ), pp. 19 - 43 . MR 364426 | Zbl 0299.20005 · Zbl 0299.20005 · doi:10.1007/BF01428252 [3] D.W. Sharpe - P. Vamos , Injective modules , Cambridge University Press , 1972 . MR 360706 | Zbl 0245.13001 · Zbl 0245.13001 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.