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Pushout complements for partly total algebras

Published online by Cambridge University Press:  08 May 2002

PETER BURMEISTER ,
MERCÈ LLABRÉS  and
FRANCESC ROSSELLÓ
PETER BURMEISTER
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany. Email: burmeister@mathematik.tu-darmstadt.de
MERCÈ LLABRÉS
Affiliation:
Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain. Email: merce@ipc4.uib.es, cesc@ipc4.uib.es
FRANCESC ROSSELLÓ
Affiliation:
Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain. Email: merce@ipc4.uib.es, cesc@ipc4.uib.es
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Abstract

Let Σ be an arbitrary signature and ϒ be a non-empty set of operation symbols within it. A (partial) Σ-algebra is ϒ-total when all its operations in ϒ are total: these are the partly total algebras in the title, and they include total algebras and attributed graphs. In this paper we establish a necessary and sufficient condition on a pair of homomorphisms of ϒ-total Σ-algebras for the existence of a pushout complement of them. This solves the application problem for the double-pushout transformation of these kinds of structure.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 12 , Issue 2 , April 2002 , pp. 177 - 201
Copyright
© 2002 Cambridge University Press

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Footnotes

This work was supported in part by the DGES, grant PB96-0191-C02-01. M. Llabrés has also been partially supported by the EU TMR Network GETGRATS through the Technische Universität Berlin and the Università di Pisa.