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1998 | 77 | 1 | 41-58
Tytuł artykułu

Equimorphy in varieties of double Heyting algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class $\Cal S$ ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive double p-algebras.
Rocznik
Tom
77
Numer
1
Strony
41-58
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-09-15
Twórcy
autor
  • MFF KU, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
autor
  • Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Bibliografia
  • [1] M. E. Adams, V. Koubek and J. Sichler, Homomorphisms and endomorphisms in varieties of pseudocomplemented distributive lattices (with applications to Heyting algebras), Trans. Amer. Math. Soc. 285 (1984), 57-79.
  • [2] V. Koubek and H. Radovanská, Algebras determined by their endomorphism monoids, Cahiers Topologie Géom. Différentielle Catégoriques 35 (1994), 187-225.
  • [3] V. Koubek and J. Sichler, Categorical universality of regular distributive double $p$-algebras, Glasgow Math. J. 32 (1990), 329-340.
  • [4] ---, ---, Priestley duals of products, Cahiers Topologie Géom. Différentielle Catégoriques 32 (1991), 243-256.
  • [5] ---, ---, Finitely generated universal varieties of distributive double $p$-algebras, ibid. 35 (1994), 139-164.
  • [6] ---, ---, Equimorphy in varieties of distributive double p-algebras, Czechoslovak Math. J., to appear.
  • [7] K. D. Magill, The semigroup of endomorphisms of a Boolean ring, Semigroup Forum 4 (1972), 411-416.
  • [8] C. J. Maxson, On semigroups of Boolean ring endomorphisms, ibid., 78-82.
  • [9] R. McKenzie and C. Tsinakis, On recovering a bounded distributive lattice from its endomorphism monoid, Houston J. Math. 7 (1981), 525-529.
  • [10] H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186-190.
  • [11] ---, Ordered sets and duality for distributive lattices, Ann. Discrete Math. 23 (1984), 36-60.
  • [12] A. Pultr and V. Trnková, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland, Amsterdam, 1980.
  • [13] B. M. Schein, Ordered sets, semilattices, distributive lattices and Boolean algebras with homomorphic endomorphism semigroups, Fund. Math. 68 (1970), 31-50.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv77z1p41bwm
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