Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T08:37:17.668Z Has data issue: false hasContentIssue false

The failure of the amalgamation property for representable varieties of l-groups

Published online by Cambridge University Press:  24 October 2008

Wayne B. Powell
Affiliation:
Oklahoma State University, Stillwater, OK 74078, U.S.A.
Constantine Tsinakis
Affiliation:
Vanderbilt University, Nashville, TN 37235, U.S.A.

Extract

A variety satisfies the amalgamation property if given G, H1, and embeddings τ1: GH1 and τ2: GH2, there exist and embeddings σ1: H1K and σ2: H2K such that σ1τ1 = σ2τ2.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bigard, A., Keimel, K. and Wolfenstein, S.. Groupes et Anneaux Réticulés. Lecture Notes in Math. vol. 608 (Springer-Verlag, 1977).CrossRefGoogle Scholar
[2]Feil, T.. An uncountable tower of l-group varieties. Algebra Universalis 14 (1982), 129131.CrossRefGoogle Scholar
[3]Glass, A. M. W., Saracino, D. and Wood, C.. Non-amalgamation of ordered groups. Math. Proc. Cambridge Philos. Soc. 95 (1984), 191195.CrossRefGoogle Scholar
[4]Kiss, E. W., Márki, L., Pröhle, P. and Tholen, W.. Categorical Algebraic Properties. A compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity. Studia Sci. Math. Hungarica 18 (1983), 79141.Google Scholar
[5]Medvedev, N. Ya.. The lattices of varieties of lattice-ordered groups and Lie algebras. Algebra and Logic 16 (1977), 2730.Google Scholar
[6]Pierce, K. R.. Amalgamations of lattice ordered groups. Trans. Amer. Math. Soc. 172 (1972), 249260.CrossRefGoogle Scholar
[7]Pierce, K. R.. Amalgamated abelian ordered groups. Pacific J. Math. 43 (1972), 711723.CrossRefGoogle Scholar
[8]Pierce, K. R.. Amalgamated sums of abelian l-groups. Pacific J. Math. 65 (1976), 167173.CrossRefGoogle Scholar
[9]Scrimger, E. B.. A large class of small varieties of lattice ordered groups. Proc. Amer. Math. Soc. 51 (1975), 301306.CrossRefGoogle Scholar
[10]Powell, W. B. and Tsinakis, C.. Free products in the class of abelian l-groups. Pacific J. Math. 104 (1983), 429442.CrossRefGoogle Scholar
[11]Powell, W. B. and Tsinakis, C.. Free products of lattice ordered groups. Algebra Universalis 18 (1984), 178198.Google Scholar
[12]Powell, W. B. and Tsinakis, C.. Amalgamations of lattice ordered groups. In Ordered Algebraic Structures, Lecture Notes in Pure and Applied Math. vol. 99 (Marcel Dekker, 1985), pp. 171178.Google Scholar