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Embedding sums of cancellative modes into functorial sums

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Języki publikacji
EN
Abstrakty
EN
The paper discusses a representation of modes (idempotent and entropic algebras)as subalgebras of so called functorial sums of cancellative algebras.We show that each mode that has a homomorphism onto an algebra satisfying a certain additional condition,with corresponding cancellative congruence classes,embeds into a functorial sum of cancellative algebras.We also discuss typical applications of this result.
Wydawca
Rocznik
Strony
557--569
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
  • Faculty Of Mathematics And Information Science Warsaw University Of Technology Plac Politechniki 1 00-661 Warsaw, Poland, aroman@mini.pw.edu.pl
Bibliografia
  • [1] J. Kuras, Application of Agassiz Systems to Representation of Sums of Equationally Defined Classes of Algebras, Ph.D. Thesis (in Polish), M. Kopernik University, Toruń, 1985.
  • [2] A. I. Mal’cev, Algebraičeskie Sistemy, [in Russian], Sovremennaja Algebra, Nauka, Moscow, 1970. English translation: Algebraic Systems, Springer Verlag, Berlin, 1973.
  • [3] A. B. Romanowska, J. D. H. Smith, Modal Theory, Heldermann Verlag, Berlin, 1985.
  • [4] A. B. Romanowska, J. D. H. Smith, On the structure of semilattice sums, Czechoslovak Math. J. 41 (1991), 24–43.
  • [5] A. B. Romanowska, J. D. H. Smith, Embedding sums of cancellative modes into functorial sums of affine spaces, in Unsolved Problems on Mathematics for the 21st Century, a Tribute to Kiyoshi Iseki’s 80th Birthday (J. M. Abe and S. Tanaka, eds.), IOS Press, Amsterdam, 2001, pp. 127–139.
  • [6] A. B. Romanowska, J. D. H. Smith, Modes, World Scientific, Singapore, 2002.
  • [7] A. B. Romanowska, J. D. H. Smith, Errata: Modes. http://orion.math.iastate.edu/jdhsmith/math/MODErata.pdf.
  • [8] A. B. Romanowska, S. Traina, Algebraic quasi-orders and sums of algebras, Discuss. Math. Algebra & Stochastic Methods 19 (1999), 239–263.
  • [9] A. B. Romanowska, A. Zamojska-Dzienio, Embedding semilattice sums of cancellative modes into semimodules, Contributions to General Algebra 13 (2001), 295–304.
  • [10] A. B. Romanowska, A. Zamojska-Dzienio, Embedding sums of cancellative modes into semimodules, Czechoslovak Math. J. 55 (2005), 975–991.
  • [11] V. N. Saliǐ, Equationally normal verieties of semigroups, (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 84 (1969), 61–68.
  • [12] V. N. Saliǐ, A theorem on homomorphisms of strong semilattices of semigroups, in The Theory of Semigroups and its Applications (V. V. Vagner ed.), Izd. Saratov. Univ. 2 (1970), 69–74.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0033-0018
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