Journal of Mathematical Sciences

, Volume 206, Issue 5, pp 597–607 | Cite as

On Values of Elements in Partially Ordered Groups

  • E. E. Shirshova


We consider properties of convex directed subgroups for the interpolation groups in which each element is a quotient of two almost orthogonal elements. A series of results on values for almost orthogonal elements in those groups is obtained. We investigate characteristics of lexicographic extensions for partially ordered groups in which each element is a quotient of two almost orthogonal elements.


Normal Subgroup Maximal Subgroup Positive Element Directed Group Convex Subgroup 
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  1. 1.
    P. Conrad, “The lattice of all convex l-subgroups of lattice-ordered group,” Czech. Math. J., 15, 101–123 (1965).MathSciNetGoogle Scholar
  2. 2.
    P. Conrad, “Representation of partially ordered Abelian groups as groups of real valued functions,” Acta Math., 116, 199–221 (1966).MATHMathSciNetGoogle Scholar
  3. 3.
    L. Fuchs, Partially Ordered Algebraic Systems, Pergamon Press, Oxford; Addison-Wesley, Reading (1963).Google Scholar
  4. 4.
    L. Fuchs, “Riesz groups,” Ann. Scu. Norm. Sup. Pisa, 19, No. 3, 1–34 (1965).MATHGoogle Scholar
  5. 5.
    A. M. W. Glass, “Polars and their application in directed interpolation groups,” Trans. Am. Math. Soc., 166, 1–25 (1972).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    V. M. Kopytov, Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).Google Scholar
  7. 7.
    S. Lang, Algebra, Addison-Wesley, Reading (1965).Google Scholar
  8. 8.
    E. E. Shirshova, “Pseudo-lattice ordered groups,” in: Groups and Modules; Game Theory [in Russian], Mosk. Obl. Ped. Inst., Moscow (1973), pp. 10–18.Google Scholar
  9. 9.
    E. E. Shirshova, “Associated subgroups of pseudo-lattice ordered groups,” in: Algebraic Systems [in Russian], Ivanov. Gos. Univ., Ivanovo (1991), pp. 78–85.Google Scholar
  10. 10.
    E. E. Shirshova, “Lexicographic extensions and pl-groups,” Fundam. Prikl. Mat., 1, No. 4, 1133–1138 (1995).MATHMathSciNetGoogle Scholar
  11. 11.
    E. E. Shirshova, “On homomorphisms of pl-group,” Fundam. Prikl. Mat., 3, No. 1, 303–314 (1997).MATHMathSciNetGoogle Scholar
  12. 12.
    E. E. Shirshova, “On groups with the almost orthogonality condition,” Commun. Algebra, 28, No. 10, 4803–4818 (2000).CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    E. E. Shirshova, “On a generalization of the notion of orthogonality and on the Riesz groups,” Math. Notes, 69, No. 1, 107–115 (2001).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Moscow Pedagogical State UniversityMoscowRussia

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