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Czechoslovak Mathematical Journal

, Volume 55, Issue 4, pp 975–991 | Cite as

Embedding Sums of Cancellative Modes into Semimodules

  • Anna Romanowska
  • Anna Zamojska-Dzienio
Article

Abstract

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.

Keywords

modes (idempotent and entropic algebras) cancellative modes sums of algebras embeddings semimodules over semirings idempotent subreducts of semimodules 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Anna Romanowska
    • 1
  • Anna Zamojska-Dzienio
    • 1
  1. 1.Faculty of Mathematics and Information SciencesWarsaw University of TechnologyWarsawPoland

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