PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1993 | 142 | 1 | 19-43
Tytuł artykułu

Finite atomistic lattices that can be represented as lattices of quasivarieties

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].
Rocznik
Tom
142
Numer
1
Strony
19-43
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-05-20
poprawiono
1992-03-03
Twórcy
  • Institute of Mathematics, Russian Academy of Sciences, Universitetskiĭ Prosp. 4, 630090 Novosibirsk, Russia
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Institute of Mathematics, Russian Academy of Sciences, Universitetskiĭ Prosp. 4, 630090 Novosibirsk, Russia
Bibliografia
  • [1] K. V. Adaricheva, A characterization of finite lattices of subsemilattices, Algebra i Logika 30 (1991), 385-404 (in Russian).
  • [2] K. V. Adaricheva and V. A. Gorbunov, Equaclosure operator and forbidden semidistributive lattices, Sibirsk. Mat. Zh. 30 (1989), 7-25 (in Russian).
  • [3] K. V. Adaricheva, W. Dziobiak and V. A. Gorbunov, The lattices of quasivarieties of locally finite quasivarieties, preprint.
  • [4] M. K. Bennett, Biatomic lattices, Algebra Universalis 24 (1987), 60-73.
  • [5] G. Birkhoff and M. K. Bennett, The convexity lattice of a poset, Order 2 (1985), 223-242.
  • [6] A. Day, Characterization of finite lattices that are bounded-homomorphic image of sublattices of free lattices, Canad. J. Math. 31 (1979), 69-78.
  • [7] W. Dziobiak, On atoms in the lattice of quasivarieties, Algebra Universalis 24 (1987), 31-35.
  • [8] R. Freese and J. B. Nation, Congruence lattices of semilattices, Pacific J. Math. 44 (1973), 51-58.
  • [9] H. Gaskill, G. Grätzer and C. R. Platt, Sharply transferable lattices, Canad. J. Math. 27 (1975), 1246-1262.
  • [10] V. A. Gorbunov, Lattices of quasivarieties, Algebra i Logika 15 (1976), 436-457 (in Russian).
  • [11] V. A. Gorbunov and V. I. Tumanov, A class of lattices of quasivarieties, ibid. 19 (1980), 59-80 (in Russian).
  • [12] V. A. Gorbunov and V. I. Tumanov, The structure of the lattices of quasivarieties, in: Trudy Inst. Mat. (Novosibirsk) 2, Nauka Sibirsk. Otdel., Novosibirsk 1982, 12-44 (in Russian).
  • [13] G. Grätzer, General Lattice Theory, Birkhäuser, Basel 1979.
  • [14] G. Grätzer and H. Lakser, A note on the implicational class generated by a class of structures, Canad. Math. Bull. 16 (1973), 603-605.
  • [15] B. Jónsson and J. B. Nation, A report on sublattices of a free lattice, in: Contributions to Universal Algebra, Szeged 1975, Colloq. Math. Soc. János Bolyai 17, 223-257.
  • [16] A. I. Mal'cev, On certain frontier questions in algebra and mathematical logic, in: Proc. Int. Congr. Mathematicians, Moscow 1966, Mir, 1968, 217-231 (in Russian).
  • [17] A. I. Mal'cev, Algebraic Systems, Springer, 1973.
  • [18] R. McKenzie, Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc. 174 (1972), 1-43.
  • [19] R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, Wadsworth and Brooks/Cole, Monterey 1987.
  • [20] V. I. Tumanov, Finite distributive lattices of quasivarieties, Algebra i Logika 22 (1983), 168-181 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv142i1p19bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.