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Direct Sums of Partial Algebras and Final Algebraic Structures

Published online by Cambridge University Press:  20 November 2018

Jürgen Schmidt
Jürgen Schmidt*
Affiliation:
Mathematisches Institut, Universität Bonn
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Słomiński (9), as well as the author (8), gave a descriptive, i.e., noncategory-theoretic, definition of the direct sum of partial algebras, i.e., the co-product in the category of partial algebras (A,ƒ), where ƒ = (ƒi)i∈I, ƒi: dom ƒi ⟶ A, dom ƒi ⊂ AKi, of fixed type A = (Ki)i∈I.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 872 - 887
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bourbaki, N., Théorie des ensembles, Chapitre 4 (Hermann, Paris, 1957).Google Scholar
2. Burmeister, P. and Schmidt, J., On the completion of partial algebras, Colloq. Math. 17 (1967), 235–245.Google Scholar
3. Felscher, W., Adjungierte Funktoren und primitive Klassen, Sitz. Ber. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1965, 445–509.Google Scholar
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6. Mitchell, B., Theory of categories (Academic Press, New York-London, 1965).Google Scholar
7. Schmidt, J., Die Charakteristik einer allgemeinen Algebra. I, II, Arch. Math. 18 (1962), 457-470; 15 (1964), 286–301.Google Scholar
8. Schmidt, J., A general existence theorem on partial algebras and its special cases, Colloq. Math. 14 (1966), 73–87.Google Scholar
9. Słomiński, J., A theory of extensions of quasi-algebras to algebras, Rozprawy Mat. 40 (1964), 63 pp.Google Scholar