Nonadmissible genealogical trees
type: Item
instance of: scholarly article
title: Nonadmissible genealogical trees
zbMATH Open document ID: 0741.05022
author: Gabriella D'Este
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1992-06-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108109
review text: 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 \(K\)).
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 2841
zbMATH Keywords: admisible words
zbMATH Keywords: genealogical tree
MaRDI profile type: Publication
cites work: Extended strings and admissible words
cites work: The indecomposable representations of the dihedral 2-groups
cites work: Q5656860
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description: scientific article; zbMATH DE number 2841