Journal of Mathematical Sciences

, Volume 97, Issue 3, pp 4162–4176 | Cite as

Abelian-regular positive semirings

  • V. V. Chermnyh
  • A. V. Mikhalev
  • E. M. Vechtomov


The theory of Abelian-regular positive semirings (arp-semirings) is developed here. This class contains all semiskewfields and all bounded distributive lattices. Bibliography: 11 titles.


Distributive Lattice Positive Semirings 
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  1. 1.
    G. Birkhoff,Lattice Theory, AMS, Providence, Rhode Island (1967).Google Scholar
  2. 2.
    E. M. Vechtomov, “Distributive lattices functionally represented by chains,”Fundament. Prikl. Mat.,2, No. 1, 93–102 (1996).MATHMathSciNetGoogle Scholar
  3. 3.
    E. M. Vechtomov, “Annihilator characterization of Boolean rings and Boolean lattices,”Mat. Zametki,53, No. 2, 15–24 (1993).MATHMathSciNetGoogle Scholar
  4. 4.
    G. Grätzer,General Lattice Theory, Akademie-Verlag, Berlin (1978).Google Scholar
  5. 5.
    A. H. Clifford and G. B. Preston,The Algebraic Theory of Semigroups, Vol. 1, AMS, Providence, Rhode Island (1964).Google Scholar
  6. 6.
    P. M. Cohn,Universal Algebra, Harper and Row, London (1965).Google Scholar
  7. 7.
    V. V. Chermnykh, “Sheaf representation of semirings,”Usp. Mat. Nauk,48, No. 5, 185–186 (1993).MATHMathSciNetGoogle Scholar
  8. 8.
    V. V. Chermnykh, “Representation of positive semirings by sections,”Usp. Mat. Nauk,47, No. 5, 193–194 (1992).MATHMathSciNetGoogle Scholar
  9. 9.
    A. Filipoiu, “Compact sheaves of lattices and normal lattices,”Math. Jpn.,36, No. 2, 381–386 (1991).MATHMathSciNetGoogle Scholar
  10. 10.
    L. Gillman and M. Jerison,Rings of Continuous Functions, Springer, New York (1976).Google Scholar
  11. 11.
    J. S. Golan,The Theory of Semirings with Applications in Mathematical and Theoretical Computer Science, Pitman, New York (1992).Google Scholar
  12. 29.
    Yu. D. Golovatyi, S. A. Nazarov, and O. A. Oleinik, “Asymptotic expansion of eigenvalues and eigenfunctions of problems of oscillations of a medium with concentrated perturbations,”Tr. Mat. Inst. im. V. A. Steklova Akad. Nauk SSSR,192, 42–60 (1990).MathSciNetGoogle Scholar
  13. 30.
    S. A. Nazarov, “Two-term asymptotics for solutions to problems with singular perturbations,”Mat. Sb.,181, No. 3, 291–320 (1990).Google Scholar
  14. 31.
    Ju. Nagel, “On equivalent normalizations in the functional spacesH μ,”Vestn. LGU, No. 7, 41–47 (1974).MATHGoogle Scholar
  15. 32.
    L. Hörmander,Linear Partial Differential Operators, Springer, Berlin (1963).Google Scholar
  16. 33.
    S. A. Nazarov and M. V. Paukshto,Discrete Models and Homogenization in Elasticity Theory [in Russian], LGU, Leningrad (1984).Google Scholar
  17. 34.
    M. V. Fedoryuk, “The Dirichlet problem for the Laplace operator in the exterior of a thin body of revolution,”Tr. Sem. Soboleva, No. 1, 113–131 (1980).MATHMathSciNetGoogle Scholar
  18. 35.
    M. V. Fedoryuk, “The asymptotics of the solutions to the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a thin cylinder,”Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 1, 167–186 (1981).MATHMathSciNetGoogle Scholar
  19. 36.
    V. G. Maz’ya, S. A. Nazarov, and B. A. Plamenevskii, “On the asymptotics for solutions to the Dirichlet problem in a three-dimensional domain with a thin cavity,”Dokl. Akad. Nauk SSSR,256, No. 1, 37–39 (1981).MathSciNetGoogle Scholar
  20. 37.
    V. G. Maz’ya, S. A. Nazarov, and B. A. Plamenevskii, “Asymptotics for solutions to the Dirichlet problem in a domain with a thin hollow tube,”Mat. Sb.,116, No. 2, 187–217 (1981).MathSciNetGoogle Scholar
  21. 38.
    J. Geer, “Electromagnetic scattering by a slender body of revolution: axially insider plane wave,”SIAM J. Appl. Math.,38, No. 1, 93–102 (1980).MATHMathSciNetGoogle Scholar
  22. 39.
    I. S. Zorin and S. A. Nazarov, “The stress-deformed state of an elastic space with a thin toroidal enclosure,”Mekh. Tverd. Tela, No. 3, 79–86 (1980).Google Scholar
  23. 40.
    I. S. Zorin, “A thin toroidal cavity in a half-bounded elastic body,” in:Issled. po Uprugosti i Plastichn., No. 15, LGU, Leningrad, 32–39 (1986).Google Scholar
  24. 41.
    G. V. Zhdanova, “Scattering of plane length-wise elastic waves by a thin cavity of revolution. Case of the axial fall,”Mat. Sb.,121, No. 3, 310–326 (1983).MATHMathSciNetGoogle Scholar
  25. 42.
    G. V. Zhdanova, “The asymptotics for the solution of the Dirichlet problem for the equations elasticity theory in the exterior of a thin body of revolution,”Mat. Sb.,134, No. 1, 3–27 (1987).MATHMathSciNetGoogle Scholar
  26. 43.
    R. V. Goldshtein, A. V. Kaptsov, and L. B. Korel’shtein, “The asymptotic solution to three-dimensional problems of elasticity theory concerning elongated plane breakaway fissures,”Prikl. Mat. Mekh.,48, No. 5, 854–863 (1984).MathSciNetGoogle Scholar
  27. 44.
    A. Bensoussan, J.-L. Lions, and G. Papanicolau,Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam (1978).Google Scholar
  28. 45.
    E. Sanchez Palencia,Nonhomogeneous Media and Vibration Theory, Lecture Notes in Physics,129, Springer, Berlin (1980).Google Scholar
  29. 46.
    N. S. Bakhvalov and G. P. Panasenko,Averaging Processes in Periodic Media, Kluwer, Dordrecht (1989).Google Scholar
  30. 47.
    O. A. Oleinik, A. S. Shamaev, and G. A. Yosifian,Mathematical Problems in Elastisity and Homogenization, Elsevier, Amsterdam (1992).Google Scholar
  31. 48.
    V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik,Homogenization of Differential Operators and Integral Functionals, Springer, Berlin (1994).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. V. Chermnyh
  • A. V. Mikhalev
  • E. M. Vechtomov

There are no affiliations available

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