Embedding sums of cancellative modes into semimodules

Anna B. Romanowska; Anna Zamojska-Dzienio

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 975-991
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Romanowska, Anna B., and Zamojska-Dzienio, Anna. "Embedding sums of cancellative modes into semimodules." Czechoslovak Mathematical Journal 55.4 (2005): 975-991. <http://eudml.org/doc/31004>.

@article{Romanowska2005,
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.},
author = {Romanowska, Anna B., Zamojska-Dzienio, Anna},
journal = {Czechoslovak Mathematical Journal},
keywords = {modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules; modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules},
language = {eng},
number = {4},
pages = {975-991},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Embedding sums of cancellative modes into semimodules},
url = {http://eudml.org/doc/31004},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Romanowska, Anna B.
AU - Zamojska-Dzienio, Anna
TI - Embedding sums of cancellative modes into semimodules
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 975
EP - 991
AB - 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.
LA - eng
KW - modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules; modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules
UR - http://eudml.org/doc/31004
ER -

References

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