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On Extensions of AO-Groups


The notion of an extension is important in the study of partially ordered groups. In the present paper the notion of a lexicographic extension of a partially ordered group by an AO-group is studied. A result is obtained concerning an AO-group G which is a lexicographic extension of a directed subgroup of G.

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  1. 1.

    V. M. Kopytov, Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  2. 2.

    L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris (1963).

    Google Scholar 

  3. 3.

    P. Conrad, “The lattice of all convex l-subgroups of lattice-ordered group,” Czechosl. Math. J., 15, 101–123 (1965).

    Google Scholar 

  4. 4.

    P. Conrad, “Representation of partially ordered Abelian groups as groups of real valued functions,” Acta Math., 116, 199–221 (1966).

    Google Scholar 

  5. 5.

    E. E. Shirshova, “On extensions of po-groups,” Contemp. Math., 131 (Part 1), 345–353 (1992).

    Google Scholar 

  6. 6.

    E. E. Shirshova, “Lexicographic extensions and pl-groups,” Fund. Prikl. Mat., 1, No.4, 1133–1138 (1995).

    MathSciNet  Google Scholar 

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 277–281, 2003.

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Shirshova, E.E. On Extensions of AO-Groups. J Math Sci 128, 3513–3515 (2005).

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  • Directed Subgroup
  • Lexicographic Extension