The algebra of mode homomorphisms

Kira Adaricheva; Anna Romanowska; Jonathan Smith

Open Mathematics (2014)

  • Volume: 12, Issue: 8, page 1265-1277
  • ISSN: 2391-5455

Abstract

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Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.

How to cite

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Kira Adaricheva, Anna Romanowska, and Jonathan Smith. "The algebra of mode homomorphisms." Open Mathematics 12.8 (2014): 1265-1277. <http://eudml.org/doc/269651>.

@article{KiraAdaricheva2014,
abstract = {Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.},
author = {Kira Adaricheva, Anna Romanowska, Jonathan Smith},
journal = {Open Mathematics},
keywords = {Mode; Convex set; Affine space; Semilattice; Variety regularization; Płonka sum; modes; semilattices; variety regularizations; Płonka sums},
language = {eng},
number = {8},
pages = {1265-1277},
title = {The algebra of mode homomorphisms},
url = {http://eudml.org/doc/269651},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Kira Adaricheva
AU - Anna Romanowska
AU - Jonathan Smith
TI - The algebra of mode homomorphisms
JO - Open Mathematics
PY - 2014
VL - 12
IS - 8
SP - 1265
EP - 1277
AB - Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.
LA - eng
KW - Mode; Convex set; Affine space; Semilattice; Variety regularization; Płonka sum; modes; semilattices; variety regularizations; Płonka sums
UR - http://eudml.org/doc/269651
ER -

References

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  7. [7] Pöschel R., Reichel M., Projection algebras and rectangular algebras, In: General Algebra and Applications, Potsdam, January 31–February 2, 1992, Res. Exp. Math., 20, Heldermann, Berlin, 1993, 180–194 Zbl0788.08007
  8. [8] Romanowska A.B., Smith J.D.H., Modal Theory, Res. Exp. Math., 9, Heldermann, Berlin, 1985 
  9. [9] Romanowska A.B., Smith J.D.H., Modes, World Scientific, Singapore, 2002 http://dx.doi.org/10.1142/4953 
  10. [10] Smith J.D.H., Romanowska A.B., Post-Modern Algebra, Pure Appl. Math. (N.Y.), John Wiley & Sons, New York, 1999 http://dx.doi.org/10.1002/9781118032589 Zbl0946.00001
  11. [11] Sokratova O., Kaljulaid U., Ω-rings and their flat representations, In: Contributions to General Algebra, 12, Vienna, June 3–6, 1999, Heyn, Klagenfurt, 2000, 377–390 Zbl0971.16024

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