References
R. Balbes andP. Dwinger, “Distributive Lattices,” University of Missouri Press, Columbia, 1974.
C. C. Chang andH. J. Keisler, “Model Theory,” North-Holland, Amsterdam, 1973.
A. H. Clifford andG. B. Preston, “The Algebraic Theory of Semigroups,” Math. Surveys No. 7, Vol. 1, Arner. Math. Soc., Providence, R. I., 1961.
W. W. Comfort andS. Negrepontis, “The Theory of Ultrafilters,” Springer-Verlag, Berlin, Heidelberg, New York, 1974.
R. A. Dean,Component subsets of the free lattice on n generators, Proc. Amer. Math. Soc.7 (1956), 220–226.
P. Erdös andA. Hajnal,On a problem of B. Jónsson, Bull. Acad. Polon. Sci.14 (1966), 19–23.
S. Fajtlowicz,A property of the lattice of subsemilattices, Colloq. Math.42 (1979), 121–122.
J. A. Green andD. Rees,On semigroups in which x r=x, Proc. Cambridge Phil. Soc.48 (1952), 35–40.
T. E. Hall,Free products with amalgamation of inverse semigroups, J. Algebra34 (1975), 375–385.
T. E.Hall,Amalgamation and inverse and regular semigroups: a brief survey, Symposium on Regular Semigroups, Northern Illinois University (1979), 49–79.
G. Higman, B. H. Neumann andH. Neumann,Embedding theorems for groups, J. London Math. Soc.24 (1949), 247–254.
B. Jönsson,Universal relational systems, Math. Scand.4 (1956), 193–208.
B. Jónsson,Homogeneous universal relational systems, Math. Scand.8 (1960), 137–142.
B. Jónsson, “Topics in Universal Algebra,” Springer-Verlag, Berlin, Heidelberg, New York, 1972.
H. J. Keisler andF. Rowbottom,Constructible sets and weakly compact cardinals, Notices Amer. Math. Soc.12 (1965), 373–374.
N. Kimura,The structure of idempotent semigroups (I), Pacific J. Math.8 (1958), 257–275.
B.Koppelberg, R.McKenzie, and J. D.Monk,Cardinality and cofinality of homomorphs of products of Boolean algebras (preprint).
S. Koppelberg,Boolean algebras as unions of chains of subalgebras, Algebra Universalis7 (1977), 195–203.
S. Koppelberg andJ. Tits,Une propriété des produits directs infinis du groupes finis isomorphes, C. R. Acad. Sci. Paris279 (1974), Série A, 583–585.
L. Y. Kulikov,On the theory of abelian groups of arbitrary cardinality [Russian], Mat. Sb.,16 (1945), 129–162.
J. Loats,On endomorphisms of Boolean algebras and other problems, Ph.D. Dissertation, Univ. of Colorado, Boulder, 1977.
A. I. Mal'Cev,On multiplication of classes of algebraic systems, Mat. Sb.35 (77) (1954), 3–20; English transl., A. M. S. Transl. (2)27 (1963), 125–142.
Anne C. Morel,Some remarks on groupoids-locally cyclic, locally finite, and Jónsson, Colloquia Mathematica Societatis Janos Bolyai29 (1982), 525–529.
M. Petrich, “Introduction to Semigroups,” Charles E. Merrill Publishing Co., Columbus, 1973.
J. PŁonka,On a method of construction of abstract algebras, Fund. Math.61 (1967), 183–189.
D. Rees,On semi-groups, Proc. Cambridge Phil. Soc.36 (1940), 387–400.
G. Sabbagh,Sur les groupes que ne sont pas réunion d'une suite crosisante de sous-groupes propres, C. R. Acad. Sci. Paris280 (1975), Serie A, 763–766.
O. Schreier,Die Untergruppen der freien Gruppen, Abh. Math. Sem. Univ. Hamburg5 (1927), 161–183.
S.Shelah,On a problem of Kurosh, Jńsson groups, and applications, Word Problems II (Conference on Decision Problems in Algebra, Oxford, 1976), 373–394.
Ju. I. Sorkin,On the imbedding of latticoids in lattices, Doklady Akad. Nauk SSSR N.S.95 (1954), 931–934.
A. Tarski andR. L. Vaught,Arithmetical extensions of relational systems, Compositio Mathematica13 (1957), 81–102.
Author information
Authors and Affiliations
Additional information
Research supported by the Vanderbilt University Research Council.
Rights and permissions
About this article
Cite this article
Gould, M., Morel, A.C. & Tsinakis, C. Cofinality of algebras. Algebra Universalis 22, 253–278 (1986). https://doi.org/10.1007/BF01224031
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01224031