Embedding semilattice sums of cancellative modes into semimodules (Q2759853)

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).NEWLINENEWLINENEWLINEA mode is a semilattice sum of cancellative modes if it has a congruence with a semilattice quotient and cancellative congruence classes.NEWLINENEWLINENEWLINEThe 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.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].