Realization theorems for valuated \(p^n\)-socles.
type: Item
instance of: scholarly article
title: Realization theorems for valuated \(p^n\)-socles.
zbMATH Open document ID: 1241.20064
DOI: 10.4171/RSMUP/126-9
author: Patrick W. Keef
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2012-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/243162
full work available at URL: http://rendiconti.math.unipd.it/volumes/vol126.php
review text: The author and colleagues have previously proved that \(n\)-summable valuated \(p^n\)-socles are isometric if and only if their Ulm functions agree. In this paper, he poses and answers three related questions:{\parindent=5mm\begin{itemize} \item[1)] Which cardinal valued functions on countable ordinals are Ulm functions of some \(n\)-summable valuated \(p^n\)-socle?\item [2)] Which \(n\)-summable valuated \(p^n\)-socles are realizable as the \(p^n\)-socles of some Abelian \(p\)-group?\item [3)] Which \(n\)-summable Abelian \(p\)-groups are determined by their Ulm functions? \end{itemize}}
reviewed by: Phillip Schultz
Mathematics Subject Classification ID: 20K10
zbMATH DE Number: 6005075
zbMATH Keywords: Abelian \(p\)-groups
zbMATH Keywords: valuated vector spaces
zbMATH Keywords: valuated \(p\)-groups
zbMATH Keywords: \(n\)-summable groups
zbMATH Keywords: Ulm functions
MaRDI profile type: Publication
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OpenAlex ID: W2004335519
description: scientific article; zbMATH DE number 6005075