LIST OF MAIN PUBLICATIONS

OF

BACHUKI MESABLISHVILI


  1. THE LATTICE OF SEPARABLE SUBALGEBRAS OF A RADICAL EXTENSION OF A CONNECTED RING.
    Bull. Georgian Acad. Sci. 126 (1987), pp.29-32.

  2. FINITE GALOIS EEXTENSIONS OF A CONNECTED RING IN AN ELEMENTARY TOPOS.
    Bull. Georgian Acad. Sci. 135 (1989), pp.32-36.

  3. FUNDAMENTAL THEOREM FOR FINITE GALOIS EXTENSIONS OF AN INTERNAL COMMUTATIVE CONNECTED RING
    IN AN ELEMENTARY TOPOS AND THE FUNCTOR $T$.
    Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 36 (1990), pp.9-27.

  4. GALOIS OBJECTS IN THE CATEGORY OF INTERNAL COMMUTATIVE ALGEBRAS IN AN ELEMENTARY TOPOS AND THEIR FLATNESS.
    Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 36 (1990), pp.28-44.

  5. GALOIS THEORY IN A CATEGORY OF MODULES OVER AN ELEMENTARY TOPOS.
    Bull. Georgian Acad. Sci. 159 (1999), pp.20-22.

  6. PURE MORPHISMS OF COMMUTATIVE RINGS ARE EFFECTIVE DESCENT MORPHISMS FOR MODULES.
    Theory and Applications of Categories 7 (2000), pp.38-42.

  7. ON SOME PROPERTIES OF PURE MORPHISMS OF COMMUTATIVE RINGS.
     Theory and Applications of Categories 10 (2002), pp.180-186.

  8. DESCENT THEORY FOR SCHEMES.
    Applied Categorical Structures 12 (2004), pp.485-512.

  9. EVERY SMALL $Sl$-ENRICHED CATEGORY IS MORITA EQUIVALENT TO AN $Sl$-MONOID.
    Theory and Applications of Categories 13 (2004), pp.169-171.

  10. MORE ON DESCENT THEORY FOR SCHEMES.
    Georgian Mathematical Journal 11(4)(2004), pp.783-800.

  11. DESCENT IN CATEGORIES OF (CO)ALGEBRAS.
    Homology, Homotopy and Applications 7(1) (2005), pp.1-8.

  12. MONADS OF EFFECTIVE DESCENT TYPE AND COMONADICITY.
    Theory and Applications of Categories 16(2006), pp.1-45.

  13. ON COMONADICITY OF THE EXTENSION-OF-SCALARS FUNCTORS.
    Journal of Algebra 305 (2006), pp.1102-1110.

  14. COMONADICITY AND INVERTIBLE BIMODULES.
    Journal of Algebra 313 (2007), pp.761-772.

  15. ENTWINING STRUCTURES IN MONOIDAL CATEGORIES.
    Journal of Algebra 319 (2008), pp.2496-2517.

  16. DESCENT IN $*$-AUTONOMOUS CATEGORIES.
    Journal of Pure and Applied Algebra 213 (2009), pp.60-70.

  17. (with R. Wisbauer)   GALOIS FUNCTORS AND ENTWINING STRUCTURES.
    Journal of Algebra 324 (2010), pp.464-506.

  18. (with R. Wisbauer)   BIMONADS AND HOPF MONADS ON CATEGORIES.
    Journal of K-Theory 7(2)     (2011), pp.349-388.

  19. EFFECTIVE CODESCENT MORPHISMS IN LOCALLY PRESENTABLE CATEGORIES.
    Journal of Mathematical Sciences Vol. 186(5) (2012), pp. 770-780.

  20. (with J. Gomez-Torrecillas)   A BICATEGORICAL VERSION OF MASUOKA'S THEOREM.
     Algebras and Representation Theory 15(1)(2012), pp. 147-194

  21. (with R. Wisbauer)   NOTES ON BIMONADS AND HOPF MONADS.
    Theory and Applications of Categories 26(2012), pp. 281–303.

  22. DESCENT IN MONOIDAL CATEGORIES.
    Theory and Applications of Categories 27(2012), pp.210-221.

  23. AZUMAY ALGEBRAS AS GALOIS COMODULES.
    Journal of Mathematical Sciences 195(2013), pp.518-522.

  24. (with R. Wisbauer)   ON RATIONAL PAIRINGS OF FUNCTORS.
    Applied Categorical Structures 21(3) (2013), pp. 249-290.

  25. PURE MORPHISMS ARE EFFECTIVE FOR MODULES.
    Applied Categorical Structures 21(6)(2013), pp. 801-809.

  26. (with R. Wisbauer)   QF FUNCTORS AND (CO)MONADS.
    Journal of Algebra 376 (2013), pp.101-122.

  27. (with R. Wisbauer)   GALOIS FUNCTORS AND GENERALISED HOPF MODULES.
    Journal of Homotopy and Related Structures 9(1) (2014), pp. 199-222.

  28.   DESCENT IN LOCALLY PRESENTABLE CATEGORIES.
    Applied Categorical Structures 22(5) (2014), pp. 715–726.

  29. (with R. Wisbauer)   AZUMAYA MONADS AND COMONADS.
    Axioms 4(1) (2015), pp. 32-70.

  30. (with M. Livernet and R. Wisbauer)   GENERALISED BIALGEBRAS AND ENTWINED MONADS AND COMONADS.
    Journal of Pure and Applied Algebra 219(8) (2015), pp. 3263–3278.

  31. (with R. Wisbauer)   THE FUNDAMENTAL THEOREM FOR WEAK BRAIDED MONADS.
    Journal of Algebra 490 (2017), pp. 55-103.

  32.  EFFECTIVE DESCENT MORPHISMS FOR BANACH MODULES.
    Journal of Algebra and Its Applications 18(5) (2018), 1850092, 6 pp.

  33. (with J. Gomez-Torrecillas )  SOME EXACT SEQUENCES ASSOCIATED WITH ADJUNCTIONS IN BICATEGORIES. APPLICATIONS.
    Transactions of the American Mathematical Society 371(12) (2019), pp. 8255-8295.

  34. ON DESCENT COHOMOLOGY.
    Transactions of A. Razmadze Mathematical Institute 173 (2019), pp. 137–155.

  35. (with N. Inassaridze, M. Khazaradze and E. V. Khmaladze )   ON ONE-WAY RING HOMOMORPHISMS.
    Algebra, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril., 177 (2020), pp. 80–86.

  36. NON-ABELIAN COHOMOLOGY VIA DESCENT COHOMOLOGY.
    Journal of Algebra and Its Applications (2020).