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Embedding Sums of Cancellative Modes into Semimodules

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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.

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Authors and Affiliations

  1. Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661, Warsaw, Poland

    Anna Romanowska & Anna Zamojska-Dzienio

Authors
  1. Anna Romanowska
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  2. Anna Zamojska-Dzienio
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The paper was written within the framework of COST Action 274. Research supported by Warsaw University of Technology under grant number 504G/1120/0008/000.

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Romanowska, A., Zamojska-Dzienio, A. Embedding Sums of Cancellative Modes into Semimodules. Czech Math J 55, 975–991 (2005). https://doi.org/10.1007/s10587-005-0081-2

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  • DOI: https://doi.org/10.1007/s10587-005-0081-2

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