PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2001 | 21 | 2 | 255-268
Tytuł artykułu

The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_{b}$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V).
Let B be the variety of Boolean algebras of type $τ_{b}: {+,·,´} → N$, where $τ_{b}(+) = τ_{b}(·) = 2$ and $τ_{b}(´) = 1$. In this paper we characterize the lattice $ℒ(B_{b})$ of all subvarieties of the biregularization of the variety B.
Kategorie tematyczne
Rocznik
Tom
21
Numer
2
Strony
255-268
Opis fizyczny
Daty
wydano
2001
otrzymano
2001-09-24
Twórcy
  • Mathematical Institute of the Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland
Bibliografia
  • [1] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York-Heidelberg-Berlin 1981.
  • [2] I. Chajda, Normally presented varieties, Algebra Universalis 34 (1995), 327-335.
  • [3] I. Chajda and K. Gazek, A Basic Course on General Algebra, TechnicalUniversity Press, Zielona Góra 2000.
  • [4] G. Grätzer, Universal Algebra (2nd edition), Springer-Verlag, New York-Heidelberg-Berlin 1979.
  • [5] B. Jónsson and E. Nelson, Relatively free products in regular varieties, Algebra Universalis 4 (1974), 14-19.
  • [6] H. Lakser, R. Padmanabhan and C.R. Platt, Subdirect decomposition of Płonka sums, Duke Math. J. 39 (1972), 485-488.
  • [7] R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, vol. 1, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, California 1987.
  • [8] J. Płonka, On a method of construction of abstract algebras, Fund. Math. 61 (1967), 183-189.
  • [9] J. Płonka, On equational classes of abstract algebras defined by regular equations, Fund. Math. 64 (1969), 241-247.
  • [10] J. Płonka, Biregular and uniform identities of bisemilattices, Demonstratio Math. 20 (1987), 95-107.
  • [11] J. Płonka, On varieties of algebras defined by identities of some special forms, Houston J. Math. 14 (1988), 253-263.
  • [12] J. Płonka, Biregular and uniform identities of algebras, Czechoslovak Math. J. 40 (115) (1990), 367-387.
  • [13] J. Płonka, Subdirect decompositions of algebras from 2-clone extension of varieties, Colloq. Math 77 (1998), 189-199.
  • [14] J. Płonka, On n-clone extensions of algebras, Algebra Universalis 40 (1998), 1-17.
  • [15] J. Płonka, Free algebras over biregularization of varieties, Acta Appl. Math. 52 (1998), 305-313.
  • [16] J. Płonka, On sums of direct systems of Boolean algebras, Colloq. Math. 20 (1969), 209-214.
  • [17] J. Płonka, Lattices of subvarieties of the clone extension of some varieties, Contributions to General Algebra 11 (1999), 161-171.
  • [18] J. Płonka, Clone networks, clone extensions and biregularizations of varieties of algebras, Algebra Colloq. 8 (2001), 327-344.
  • [19] J. Płonka. and Z. Szylicka, Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras, Algebra Universalis (in print).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1042
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.