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1993 | 28 | 1 | 239-252
Tytuł artykułu

Discriminator varieties of Boolean algebras with residuated operators

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated monoids are discriminator algebras, provided they are subdirectly irreducible. These results are then used to give equational bases for some varieties of r-algebras. We also show that the variety of all residuated Boolean monoids is not a discriminator variety, which answers a question of B. Jónsson.
Słowa kluczowe
Rocznik
Tom
28
Numer
1
Strony
239-252
Opis fizyczny
Daty
wydano
1993
Twórcy
autor
  • Department of Mathematics, Iowa State University, 400 Carver Hall, Ames, Iowa 50011, U.S.A.
Bibliografia
  • [BP89] W. J. Blok and D. Pigozzi, On the structure of varieties with equationally definable principal congruences III, preprint, 1989.
  • [GM90] S. Ghilardi and G. C. Meloni, Modal logics with n-ary connectives, Z. Math. Logik Grundlag. Math. 36 (1990), 193-215.
  • [J91] B. Jónsson, The preservation theorem for canonical extensions of Boolean algebras with operators, in: Proc. Birkhoff Sympos., to appear.
  • [J91a] B. Jónsson, Boolean algebras with operators, in: Proc. 1991 Summer Session 'Algebras and order' at the Université de Montréal, Kluwer, to appear.
  • [JT51] B. Jónsson and A. Tarski, Boolean algebras with operators, Part I, Amer. J. Math. 73 (1951), 891-939.
  • [JTs91] B. Jónsson and C. Tsinakis, Relation algebras as residuated Boolean algebras, Algebra Universalis, to appear.
  • [Ma78] R. Maddux, Topics in relation algebras, doctoral dissertation, Univ. of California, Berkeley 1975.
  • [Ma82] R. Maddux, Some varieties containing relation algebras, Trans. Amer. Math. Soc. 272 (2) (1982), 501-526.
  • [M75] R. McKenzie, On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model, J. Symbolic Logic 40 (2) (1975), 186-196.
  • [MMT] R. N. McKenzie, G. F. McNulty and W. F. Taylor, Algebras, Lattices, Varieties, Volume I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth, Belmont, California, 1987.
  • [P61] W. Prenowitz, A contemporary approach to classical geometry, Amer. Math. Monthly 68 (No. 1, Part II) (1961).
  • [W78] H. Werner, Discriminator algebras, Stud. Algebra Anwendungen 6, Akademie-Verlag, Berlin 1978.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv28z1p239bwm
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