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Embedding semilattice sums of cancellative modes into semimodules. (English) Zbl 0993.08004

Chajda, I. (ed.) et al., Contributions to general algebra 13. Proceedings of the 60th workshop on general algebra “60. Arbeitstagung Allgemeine Algebra”, Dresden, Germany, June 22-25, 2000 and of the summer school ’99 on general algebra and ordered sets, Velké Karlovice, Czech Republic, August 30-September 4, 1999. Klagenfurt: Verlag Johannes Heyn. Contrib. Gen. Algebra. 13, 295-303 (2001).
Algebras called modes originated as a common generalization of affine spaces, convex sets and semilattices. They are characterized by two basic properties: idempotent (in the sense that each singleton is a subalgebra) and entropic (i.e. each operation of a mode is actually a morphism of the appropriate power of the algebra).
A mode is a semilattice sum of cancellative modes if it has a congruence with a semilattice quotient and cancellative congruence classes.
The main result of this paper reads that each semilattice sum of cancellative modes embeds as a subreduct into a Płonka sum of affine spaces. As a corollary, one obtains an embedding of such semilattice sums into semimodules.
For the entire collection see [Zbl 0970.00014].

MSC:

08A05 Structure theory of algebraic structures
16Y60 Semirings
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