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On direct limits of finite algebras. (English) Zbl 0931.08005
Chajda, I. (ed.) et al., Contributions to general algebra 11. Proceedings of the Olomouc workshop ’98 on general algebra, “56. Arbeitstagung Allgemeine Algebra”, Olomouc, Czech Republic, June 12–14, 1998 and of the summer school ’98 on universal algebra and ordered sets, Velké Karlovice, Czech Republic, August 31–September 5, 1998. Klagenfurt: Verlag Johannes Heyn. 101-103 (1999).
It is proved that any directed colimit of copies of finite algebras $$A_1,\dots,A_n$$, $$n\in\mathbb N$$, is isomorphic to a retract of some $$A_i$$, $$i=1,\dots,n$$.
For the entire collection see [Zbl 0914.00059].
Reviewer: J.Rosický (Brno)

MSC:
 08C05 Categories of algebras 08B25 Products, amalgamated products, and other kinds of limits and colimits 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
Keywords:
finite algebra; directed colimit; retract