Nonadmissible genealogical trees (Q1813160)

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 \(K\)).