Pacific Journal of Mathematics

Free products in the class of abelian $l$-groups.

Wayne B. Powell and Constantine Tsinakis

Article information

Source
Pacific J. Math., Volume 104, Number 2 (1983), 429-442.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102723673

Mathematical Reviews number (MathSciNet)
MR684301

Zentralblatt MATH identifier
0501.06009

Subjects
Primary: 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]
Secondary: 06F25: Ordered rings, algebras, modules {For ordered fields, see 12J15; see also 13J25, 16W80}

Citation

Powell, Wayne B.; Tsinakis, Constantine. Free products in the class of abelian $l$-groups. Pacific J. Math. 104 (1983), no. 2, 429--442. https://projecteuclid.org/euclid.pjm/1102723673


Export citation

References

  • [1] M. E. Adams and D. Kelly, Chain conditions in free products of lattices, Algebra Universalis, 7 (1977), 235-243.
  • [2] M. E. Adams and D. Kelly, Disjointness conditions infree products of lattices, Algebra Universalis, 7 (1977),245-258.
  • [3] I. Amemiya, Countable decomposability of vector lattices, J. Fac. Hokkaido Univ., 19 (1966), 111-113.
  • [4] R. Balbes, Projective and infective distributive lattices, Pacific J. Math., 21 (1967), 405-420.
  • [5] A. Bigard, Free lattice-orderedmodules, Pacific J. Math., 49 (1973), 1-6.
  • [6] A. Bigard, K. Keimel, and S. Wolfenstein, Groupes et Anneaux Reticules, Springer- Verlag, New York, Heidelberg, Berlin, 1977.
  • [7] R. D. Bleier, Free l-groups and vector lattices, J. Austral. Math. Soc, 19 (1975), 337-342.
  • [8] P. Conrad, Lattice ordered groups, Tulane University, 1970.
  • [9] P. Conrad, Free lattice-orderedgroups, J. Algebra, 16 (1970), 191-203.
  • [10] J. D. Franchello, Sublattices of free products of lattice ordered groups, Algebra Universalis, 8 (1978), 101-110.
  • [11] L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press, Oxford,1963.
  • [12] F. Galvin and B. Jnsson, Distributive sublattices of afree lattice, Canad. J. Math., 13 (1961), 265-272.
  • [13] G. Gratzer, Universal Algebra, 2nd ed., Springer-Verlag, New York, Heidelberg, Berlin, 1979.
  • [14] G. Gratzer and H. Lakser, Chain conditions in distributive free products of lattices, Trans. Amer. Math. Soc, 144 (1969), 301-312.
  • [15] G. Gratzer and J. Sichler, Free decompositions of a lattice, Canad. J. Math., 28 (1975), 276-285.
  • [16] W. C. Holland and E. Scrimger, Free products of lattice ordered groups, Algebra Universalis, 2 (1972), 247-254.
  • [17] A. Horn, A property of free Boolean algebrs, Proc. Amer. Math. Soc, 19 (1968), 142-143.
  • [18] R. E. Johnson, Free products in varieties of ordered semigroups, Proc Amer. Math. Soc, 19 (1968), 697-700.
  • [19] B. Jnsson, Sublattices of afree lattice, Canad. J. Math., 13 (1961), 256-264.
  • [20] B. Jnsson, Varieties of lattices: Some openproblems, Colloq. Math. Soc Janos Bolyai (to appear).
  • [21] H. Lakser, Disjointness condition infree products of distributive lattices: an application of Ramsey's theorem, Proc Univ. of Houston Lattice Theory Conference, Houston, 1973, 156-168.
  • [22] J. Martinez, Free products in varieties of lattice ordered groups, Czech. Math. J., 22 (97) (1972), 535-553.
  • [23] J. Martinez, Free products of abelian l-groups,Czech. Math. J., 23 (98) (1973), 349-361.
  • [24] K. R. Pierce, Amalgamations of lattice ordered groups, Trans. Amer. Math. Soc,172 (1972), 249-260.
  • [25] R. S. Pierce, Introduction to the Theory of Abstract Algebras, Holt, Rinehart, and Winston, New York, 1968.
  • [26] W. B. Powell, Projectives in a class of lattice orderedmodules, Algebra Universalis, 13 (1981), 24-40.
  • [27] W. B. Powell and C. Tsinakis, The distributive latticefree product as a sublattice of the abelian l-group free product, J. Austral. Math. Soc, (to appear).
  • [28] N. Sanin, O proizedenii topologiceskih prostranstv, Trudy Mat. Inst. Steklov. 24 (1948).
  • [29] D.Topping, Some homologicalpathology in vector lattices, Canad. J. Math., 17 (1965), 411-428.
  • [30] A. A. Vinogradov, On thefree product of ordered groups, (Russian) Mat. Sbornik, 25 (1949), 163-168.
  • [31] E. C. Weinberg,Free lattice-ordered abeliangroups, Math. Ann., 151 (1963), 187-199.
  • [32] E. C. Weinberg, Free lattice-orderedabelian groups II, Math. Ann., 159 (1965), 217-222.