Equimorphy in varieties of double Heyting algebras

V. Koubek; J. Sichler

Colloquium Mathematicae (1998)

  • Volume: 77, Issue: 1, page 41-58
  • ISSN: 0010-1354

Abstract

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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 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.

How to cite

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Koubek, V., and Sichler, J.. "Equimorphy in varieties of double Heyting algebras." Colloquium Mathematicae 77.1 (1998): 41-58. <http://eudml.org/doc/210576>.

@article{Koubek1998,
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 $\mathcal \{S\}$ ⊆ 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.},
author = {Koubek, V., Sichler, J.},
journal = {Colloquium Mathematicae},
keywords = {categorical universality; variety; double Heyting algebra; endomorphism monoid; equimorphy; finitely generated variety},
language = {eng},
number = {1},
pages = {41-58},
title = {Equimorphy in varieties of double Heyting algebras},
url = {http://eudml.org/doc/210576},
volume = {77},
year = {1998},
}

TY - JOUR
AU - Koubek, V.
AU - Sichler, J.
TI - Equimorphy in varieties of double Heyting algebras
JO - Colloquium Mathematicae
PY - 1998
VL - 77
IS - 1
SP - 41
EP - 58
AB - 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 $\mathcal {S}$ ⊆ 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.
LA - eng
KW - categorical universality; variety; double Heyting algebra; endomorphism monoid; equimorphy; finitely generated variety
UR - http://eudml.org/doc/210576
ER -

References

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  1. [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. Zbl0523.06015
  2. [2] V. Koubek and H. Radovanská, Algebras determined by their endomorphism monoids, Cahiers Topologie Géom. Différentielle Catégoriques 35 (1994), 187-225. Zbl0820.08002
  3. [3] V. Koubek and J. Sichler, Categorical universality of regular distributive double p -algebras, Glasgow Math. J. 32 (1990), 329-340. Zbl0714.18002
  4. [4] ---, ---, Priestley duals of products, Cahiers Topologie Géom. Différentielle Catégoriques 32 (1991), 243-256. 
  5. [5] —, —, Finitely generated universal varieties of distributive double p -algebras, ibid. 35 (1994), 139-164. Zbl0905.06008
  6. [6] ---, ---, Equimorphy in varieties of distributive double p-algebras, Czechoslovak Math. J., to appear. Zbl0952.06013
  7. [7] K. D. Magill, The semigroup of endomorphisms of a Boolean ring, Semigroup Forum 4 (1972), 411-416. 
  8. [8] C. J. Maxson, On semigroups of Boolean ring endomorphisms, ibid., 78-82. Zbl0262.06011
  9. [9] R. McKenzie and C. Tsinakis, On recovering a bounded distributive lattice from its endomorphism monoid, Houston J. Math. 7 (1981), 525-529. Zbl0492.06009
  10. [10] H. A. Priestley, Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186-190. Zbl0201.01802
  11. [11] ---, Ordered sets and duality for distributive lattices, Ann. Discrete Math. 23 (1984), 36-60. 
  12. [12] A. Pultr and V. Trnková, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland, Amsterdam, 1980. 
  13. [13] B. M. Schein, Ordered sets, semilattices, distributive lattices and Boolean algebras with homomorphic endomorphism semigroups, Fund. Math. 68 (1970), 31-50. Zbl0197.28902

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