Duality for some free modes

Krzysztof J. Pszczoła; Anna B. Romanowska; Jonathan D.H. Smith

Discussiones Mathematicae - General Algebra and Applications (2003)

  • Volume: 23, Issue: 1, page 45-61
  • ISSN: 1509-9415

Abstract

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The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.

How to cite

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Krzysztof J. Pszczoła, Anna B. Romanowska, and Jonathan D.H. Smith. "Duality for some free modes." Discussiones Mathematicae - General Algebra and Applications 23.1 (2003): 45-61. <http://eudml.org/doc/287722>.

@article{KrzysztofJ2003,
abstract = {The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.},
author = {Krzysztof J. Pszczoła, Anna B. Romanowska, Jonathan D.H. Smith},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {duality; modes; affine spaces and their subreducts; barycentric algebras; convex sets; simplices; hypercubes; affine space; varieties of modes},
language = {eng},
number = {1},
pages = {45-61},
title = {Duality for some free modes},
url = {http://eudml.org/doc/287722},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Krzysztof J. Pszczoła
AU - Anna B. Romanowska
AU - Jonathan D.H. Smith
TI - Duality for some free modes
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2003
VL - 23
IS - 1
SP - 45
EP - 61
AB - The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.
LA - eng
KW - duality; modes; affine spaces and their subreducts; barycentric algebras; convex sets; simplices; hypercubes; affine space; varieties of modes
UR - http://eudml.org/doc/287722
ER -

References

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  3. [3] B. Csákány, Varieties of affine modules, Acta Sci Math. 37 (1975), 3-10. 
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  13. [13] W.D. Neumann, On the quasivariety of convex subsets of affine spaces, Arch. Math. 21 (1970), 11-16. Zbl0194.01502
  14. [14] K. Pszczoła, Duality for affine spaces over finite fields, Contributions to General Algebra 13 (2001), 285-293. Zbl0993.08008
  15. [15] K.J. Pszczoła, A.B. Romanowska and J.D.H. Smith, Duality for quadrilaterals, Contribution to General Algebra, to appear. Zbl1049.08001
  16. [16] A.B. Romanowska, Barycentric algebras, 'General Algebra and Applications', Shaker Verlag, Aachen 2000, 167-181. 
  17. [17] A.B. Romanowska and J.D.H. Smith, Modal Theory, Heldermann-Verlag, Berlin 1985. 
  18. [18] A.B. Romanowska and J.D.H. Smith, Semilattice-based dualities, Studia Logica 56 (1996), 225-261. Zbl0854.08007
  19. [19] A.B. Romanowska and J.D.H. Smith, Duality for semilattice representations, J. Pure Appl. Algebra 115 (1997), 289-308. Zbl0872.18001
  20. [20] A.B. Romanowska and J.D.H. Smith, Embedding sums of cancellatice modes into functorial sums of affine spaces, 'Unsolved Problems on Mathematics for the 21st Century, a Tribute to Kiyoshi Iseki's 80th Birthday', IOS Press, Amsterdam 2001, 127-139. 
  21. [21] A.B. Romanowska and J.D.H. Smith, Modes, World Scientific, Singapore 2002. 
  22. [22] A.B. Romanowska and J.D.H. Smith, Poset extensions, convex sets, and semilattice presentations, preprint, 2002. Zbl1112.06002
  23. [23] J.D.H. Smith and A. B. Romanowska, Post-Modern Algebra, Wiley, New York, NY, 1999. 

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