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Duality for some free modes

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Abstrakty
EN
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.
Twórcy
  • Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland
  • Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland
  • Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.
Bibliografia
  • [1] R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, MO, 1974.
  • [2] D.M. Clark and B.A. Davey, Natural Dualities for the Working Algebraists, Cambridge University Press, Cambridge 1998.
  • [3] B. Csákány, Varieties of affine modules, Acta Sci Math. 37 (1975), 3-10.
  • [4] B.A. Davey, Duality theory on ten dollars a day, 'Algebras and Orders', Kluwer Acad. Publ. 1993, 71-111.
  • [5] B.A. Davey and R.W. Quackenbush, Bookkeeping duality for paraprimal algebras, Contributions to General Algebra 9 (1995), 19-26.
  • [6] B.A. Davey and H. Werner, Dualities and equivalences for varieties of algebras, Colloq. Math. Soc. J. Bolyai 33 (1980), 101-275.
  • [7] G. Grätzer, Universal Algebra, Springer-Verlag, Berlin 1979.
  • [8] K.H. Hofmann, M. Mislove and A. Stralka, The Pontryagin Duality of Compact 0-Dimensional Semilattices and its Applications, Springer-Verlag,Berlin 1974.
  • [9] J. Jezek and T. Kepka, Free commutative idempotent abelian groupoids and quasigroups, Acta Univ. Carolin. Math. Phys. 17 (1976), 13-19.
  • [10] J. Jezek and T. Kepka, Medial Groupoids, Academia, Praha 1983.
  • [11] S. MacLane, Categories for the Working Mathematician, Springer-Verlag, Berlin 1971.
  • [12] A. I. Mal'cev, Algebraic Systems, Springer-Verlag, New York 1973.
  • [13] W.D. Neumann, On the quasivariety of convex subsets of affine spaces, Arch. Math. 21 (1970), 11-16.
  • [14] K. Pszczoła, Duality for affine spaces over finite fields, Contributions to General Algebra 13 (2001), 285-293.
  • [15] K.J. Pszczoła, A.B. Romanowska and J.D.H. Smith, Duality for quadrilaterals, Contribution to General Algebra, to appear.
  • [16] A.B. Romanowska, Barycentric algebras, 'General Algebra and Applications', Shaker Verlag, Aachen 2000, 167-181.
  • [17] A.B. Romanowska and J.D.H. Smith, Modal Theory, Heldermann-Verlag, Berlin 1985.
  • [18] A.B. Romanowska and J.D.H. Smith, Semilattice-based dualities, Studia Logica 56 (1996), 225-261.
  • [19] A.B. Romanowska and J.D.H. Smith, Duality for semilattice representations, J. Pure Appl. Algebra 115 (1997), 289-308.
  • [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] A.B. Romanowska and J.D.H. Smith, Modes, World Scientific, Singapore 2002.
  • [22] A.B. Romanowska and J.D.H. Smith, Poset extensions, convex sets, and semilattice presentations, preprint, 2002.
  • [23] J.D.H. Smith and A. B. Romanowska, Post-Modern Algebra, Wiley, New York, NY, 1999.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1063
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