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On injectives in some varieties of Ockham algebras

Published online by Cambridge University Press:  18 May 2009

Teresa Almada
Teresa Almada
Affiliation:
Dep. De MatematicaFac. Ciėncias De LisboaR. Ernesto de Vasconcelos, Bloco C11700 Lisboa, Portugal
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The study of bounded distributive lattices endowed with an additional dual homomorphic operation began with a paper by J. Berman [3]. Subsequently these algebras were called distributive Ockham lattices and an order-topological duality theory for them was developed by A. Urquhart [12]. In [9], M. S. Goldberg extended this theory and described the injective algebras in the subvarieties of the variety O of distributive Ockham algebras which are generated by a single subdirectly irreducible algebra. The aim here is to investigate some elementary properties of injective algebras in join reducible members of the lattice of subvarieties of Kn,1 and to give a complete description of injectivealgebras in the subvarieties of the Ockham subvariety defined by the identity x Λ f2n(x) = x.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 345 - 351
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Balbes, R. and Dwinger, P., Distributive lattices (University of Missouri Press, 1974).Google Scholar
2.Beazer, R., Injectives in some small varieties of Ockham algebras, Glasgow Math. J. 25 (1984), 183–191.Google Scholar
3.Berman, J., Distributive lattices with an additional unary operation, Aequationes Math. 16 (1977), 165–171.Google Scholar
4.Blyth, T. S. and Varlet, J. C., On a common abstraction of de Morgan algebras and Stone algebras, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 301–308.Google Scholar
5.Cignoli, R., Injective De Morgan and Kleene algebras, Proc. Amer. Math. Soc., 47 (1975), 269–278.Google Scholar
6.Davey, B. A., Weak injectivity and congruence extension in congruence-distributive equational classes, Canad. J. Math. XXIX (3) (1977), 449–459.Google Scholar
7.Davey, B. A. and Werner, H., Injectivity and Boolean powers, Math. Z. 166 (1979), 205–223.Google Scholar
8.Day, A., Injectivity in equational classes of algebras, Canad. J. Math. XXIV (2) (1972), 209–220.Google Scholar
9.Goldberg, M. S., Distributive Ockham algebras: free algebras and injectivity, Bull. Austral. Math. Soc., 24 (1981), 161–203.Google Scholar
10.Ramalho, M. and Sequeira, M., On generalized MS-algebras, Portugal. Math. 44 (3) (1987), 315–328.Google Scholar
11.Sequeira, M., Varieties of Ockham algebras satisfying x ≤ f n(x), Portugal. Math.. 45 (4) (1988), 369–391.Google Scholar
12.Urquhart, A., Distributive lattices with a dual homomorphic operation, Studia Logica 38 (1979), 201–209.Google Scholar