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The distributive lattice free product as a sublattice of the abelian l-group free product

Published online by Cambridge University Press:  09 April 2009

Wayne B. Powell
Affiliation:
Oklahoma State UniversityStillwater, Oklahoma 74078, U.S.A.
Constantine Tsinakis
Affiliation:
Vanderbilt UniversityNashville, Tennessee, U.S.A.
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Abstract

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This paper establishes an important link between the class of abelian l-groups and the class of distributive lattices with a distinguished element. This is accomplished by describing the distributive lattice free product of a family of abelian l-groups as a naturally generated sublattice of their abelian l-group free product.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1983

References

Balbes, R. and Dwinger, Ph. (1974), Distributive lattices (University of Missouri Press, Columbia).Google Scholar
Bernau, S. (1969). ‘Free abelian lattice groups’. Math. Ann. 180, 4859.CrossRefGoogle Scholar
Bigard, A., Keimel, K. and Wolfenstein, S. (1977), Groupes et anneaux réticulés (Springer-Verlag, New York, Heidelberg, Berlin).CrossRefGoogle Scholar
Birkhoff, G. (1967). Lattice theory. 3rd ed. (Amer. Math. Soc. Colloq. Publ. 25, Providence).Google Scholar
Conrad, P. (1970). Lattice ordered groups (Tulane University. New Orleans).Google Scholar
Franchello, J. D. (1978), ‘Sublattices of free products of lattice ordered groups’, Algebra Universalis 8. 101110.CrossRefGoogle Scholar
Fuchs, L. (1963). Partially ordered algebraic systems (Pergamon Press, Oxford).Google Scholar
Grätzer, G. (1970). Lattice theory, first concepts and distributive lattices (Freeman, San Francisco).Google Scholar
Grätzer, G. (1979). Universal algebra, 2nd ed. (Springer-Verlag, New York, Heidelberg, Berlin).CrossRefGoogle Scholar
Holland, W. C. and Scrimger, E. (1972), ‘Free products of lattice ordered groups’. Algebra Universalis 2. 247254.CrossRefGoogle Scholar
Mal'cev, A. I. (1973), Algebraic systems (Springer-Verlag. New York, Heidelberg, Berlin).CrossRefGoogle Scholar
Martinez, J. (1972). ‘Free products in varieties of lattice ordered groups’. Czechoslovak Math. J. 22 (97), 535553.CrossRefGoogle Scholar
Martinez, J. (1973). ‘Free products of abelian l-groups’, Czechosloval. Math. J. 23 (98), 349361.CrossRefGoogle Scholar
Pierce, R. S. (1968), Introduction to the theory of abstract algebras (Holt, Rinehart, and Winston, New York).Google Scholar
Powell, W. B. and Tsinakis, C. (1981), ‘Free products in the class of abelian lattice ordered groups’, preprint.Google Scholar