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Embedding sums of cancellative modes into semimodules. (English) Zbl 1081.08003

Summary: A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.

MSC:

08A05 Structure theory of algebraic structures
03C05 Equational classes, universal algebra in model theory
08C15 Quasivarieties
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References:

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