Medial modes and rectangular algebras

Anna Zamojska-Dzienio

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 1, page 21-34
  • ISSN: 0010-2628

Abstract

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Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results of A. Romanowska, J.D.H. Smith and A. Zamojska-Dzienio.

How to cite

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Zamojska-Dzienio, Anna. "Medial modes and rectangular algebras." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 21-34. <http://eudml.org/doc/249873>.

@article{Zamojska2006,
abstract = {Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results of A. Romanowska, J.D.H. Smith and A. Zamojska-Dzienio.},
author = {Zamojska-Dzienio, Anna},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules; modes; cancellative modes; embeddings; semimodules over semirings},
language = {eng},
number = {1},
pages = {21-34},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Medial modes and rectangular algebras},
url = {http://eudml.org/doc/249873},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Zamojska-Dzienio, Anna
TI - Medial modes and rectangular algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 1
SP - 21
EP - 34
AB - Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results of A. Romanowska, J.D.H. Smith and A. Zamojska-Dzienio.
LA - eng
KW - modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules; modes; cancellative modes; embeddings; semimodules over semirings
UR - http://eudml.org/doc/249873
ER -

References

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  13. Romanowska A.B., Traina S., Algebraic quasi-orders and sums of algebras, Discuss. Math. Algebra Stochastic Methods 19 (1999), 239-263. (1999) Zbl0949.08001MR1709970
  14. Romanowska A.B., Zamojska-Dzienio A., Embedding semilattice sums of cancellative modes into semimodules, Contributions to General Algebra 13 (2001), 295-304. (2001) Zbl0993.08004MR1854593
  15. Romanowska A.B., Zamojska-Dzienio A., Embedding sums of cancellative modes into semimodules, Czechoslovak Math. J. 55 4 (2005), 975-991. (2005) Zbl1081.08003MR2184378
  16. Zamojska-Dzienio A., Embedding modes into semimodules (in English), Ph.D. Thesis, Warsaw University of Technology, Warszawa, 2003. 

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