Geodesic
Embedding sums of cancellative modes into semimodules
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 975-991

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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.
Classification : 03C05, 08A05, 08C15
Keywords: modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules 
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     title = {Embedding sums of cancellative modes into semimodules},
     journal = {Czechoslovak Mathematical Journal},
     pages = {975--991},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2005},
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     zbl = {1081.08003},
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Romanowska, Anna; Zamojska-Dzienio, Anna. Embedding sums of cancellative modes into semimodules. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 975-991. http://geodesic.mathdoc.fr/item/CMJ_2005__55_4_a13/