Pushout complements for partly total algebras

Authors:
Peter Burmeister;Mercè Llabrés;Francesc Rosselló
Affiliations:
Fachbereich Mathematik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany. Email: burmeister@mathematik.tu-darmstadt.de;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;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
Venue:
Mathematical Structures in Computer Science
Year:
2002

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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.