ArticleOriginal scientific text

Title

Equimorphy in varieties of double Heyting algebras

Authors 1, 2

Affiliations

  1. MFF KU, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
  2. Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Abstract

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 CalS ⊆ 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.

Keywords

categorical universality, variety, double Heyting algebra, endomorphism monoid, equimorphy

Bibliography

  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.
Pages:
41-58
Main language of publication
English
Received
1997-09-15
Published
1998
Exact and natural sciences