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Забавський Богдан Володимирович

Професор, доктор фізико-математичних наук,
завідувач кафедрою алгебри і логіки
механіко-математичного факультету
Львівського національного університету імені Івана Франка,
керівник наукового семінару «The Problems of Elementary Divisor Rings»,
керівник Львівського алгебраїчного семінару,
e-mail: zabavskii at gmail.com

1 Universytetska Str.
79000 Lviv, Ukraine
e-mail: zabavskii at gmail.com

 Motto

Give hope to those who lost hope

 Curriculum Vitae

Birthdate: August 19, 1957
Place of birth: Lviv, Ukraine
Citizenship: Ukraine

 Research Interests  

Rings, Ideals and Modules, K-Theory, Problems of elemenary divisor rings, Linear Algebra,

 List of Publications

Books and Monographs

  1. Zabavsky B.V. Diagonal reduction of matrices over rings // Mathematical Studies, Monograph Series, volume XVI, VNTL Publishers, 2012. Lviv. 251 pp.
  2. Zabavsky B.V., Andriychuk V.I. General Algebra // - Lviv, 2008. 225 pp. (in Ukrainian)
  3. Zabavsky B.V., Andriychuk V.I. Linear Algebra // - Lviv, 2008. 225 pp. (in Ukrainian)
  4. Zabavsky B.V., Andriychuk V.I. Algebra and Number Theory // - Lviv, 2005. 141 pp. (in Ukrainian)

Articles and Conference Reports

  1. Zabavsky B.V. Rings of Dyadic range 1 // arXiv:1702.03441v1 [math.RA] 11 Feb 2017.
  2. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // Communications in Algebra, 2016.
  3. Zabavsky B.V. Type conditions of stable range for identification of qualitative generalized classes of rings // arXiv:1508.07418v1 [math.RA] 19 Apr 2016.
  4. Zabavsky B.V., Bokhonko V.V. Bringing matrixes canonical diagonal form reversible Toeplitz matrixes // Bulletin of Donetsk National University. Series A. Natural Sciences. – 2015. – №1-2. – P. 7 – 11.
  5. Zabavsky B.V., Pihura O. Commutative morphic rings of stable range 2 // Proc. Intern. Geom. Center 2015 8(3-4), pp. 65-68
  6. Zabavsky B.V., Gatalevych A.I. New characterizations of commutative clean rings // Matematychni Studii, -2015. -V.44, No 2. pp. 115-118.
  7. Zabavsky B.V., Pihura O. Gelfand local Bezout domains are elementary divisor rings // Carpathian Math. Publ. 2015, 7 (2), pp. 188–190.
  8. Zabavsky B.V., Pihura O. A morphic ring of neat range one // Algebra and Discrete Mathematics, -2015. Vol. 20, No 2. pp. 325-329.
  9. Zabavsky B.V. K-theoretical aspect theory of the rings and modules // Спільне засідання Відділення математики НАН України і секції математики та математичного моделювання Західного наукового центру НАН України та МОН України до 90-ої річниці від народження професора Петра Степановича Казімірського, Lviv, 23 October, 2015.
  10. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // arXiv:1508.07418v1 [math.RA] 29 Aug 2015.
  11. Zabavsky B.V., Gatalevych A.I. A commutative Bezout PM domain is an elementary divisor ring // Algebra and Discrete Mathematics, -2015. Vol. 19, No 2. pp. 295-301.
  12. Zabavsky B.V., Kuznitska B.M. Avoidable rings  (Ukrainian, English) // Matematychni Studii, -2015. -V.43, No 2. pp. 153-155.
  13. Zabavsky B.V., Pihura O. Bezout morphic rings // Visnyk of the Lviv Univ. Series Mech. Math. 2014. Issue 79. P. 163-168
  14. Zabavsky B.V. Questions related to the K-theoretical aspect of Bezout rings with various stable range conditions // Mat. Stud., -2014. -V.42, № 1. pp. 89-103.
  15. Zabavsky B.V., Kuznitska B.M. Effective ring // Algebra and Discrete Mathematics, -2014. Vol. 18, No 1. pp. 151-158.
  16. Zabavsky B.V., Kuznitska B.M. A stable range of class full matrices over elementary divisor ring (in Ukrainian, in English) // Ukrainian Mathematical Journal, -2014. Vol. 66, No. 5, pp. 697–700 (in Ukrainian).
  17. Zabavsky B.V. A sharp Bezout domain is an elementary divisor ring (in Ukrainian, in English) // Ukrainian Mathematical Journal, -2014. Vol. 66, No. 2, pp. 284–288.
  18. Zabavsky B.V. Diagonal reduction of matrices over finite stable range rings // Matematychni Studii, -2014. -V.41, No 1. pp. 101-108.
  19. Zabavsky B.V. Diagonal reduction of matrices over finite stable range rings // 9-th International Algebraic Conference in Ukraine, Lviv, Ukraine, 8-13 July 2013
  20. Zabavsky B.V., Gatalevych A.I. Fractionally IF-Bezout ring // Visnyk of the Lviv Univ. Series Mech. Math. 2013. Issue 78. P. 31–35 (in Ukrainian)
  21. Zabavsky B.V., Romaniv O.M. Elementary reduction of matrices over commutative Bezout ring with n-fold stable range 2 // Applied Problems of Mechanics and Mathematics, -2013. Vol. 11.,  pp. 41-44 (in Ukrainian).
  22. Zabavsky B.V., Domsha O., Kysil T. Reduction of matrices over Bezout domains of stable range 1 with Dubrovins condition in which maximal nonprincipal ideals are two-sides // Algebra and Discrete Mathematics, -2012. Vol. 14, No 2. pp. 230-235.
  23. Zabavsky B.V., Zelisko H.V., Kysil T. On the right Bezout ring with finite stable range // Math. Bull. of the Shev. Sc. Soc., -2012, Vol.9, pp.124-128 (in Ukrainian).
  24. Zabavsky B.V. A commutative Bezout domain in which every maximal ideal is principal is an elementary divisor ring // arXiv:1210.8104 [math.RA], 30 Oct 2012.
  25. Zabavsky B.V., Vasyunyk I.S. Stable rang adequate duo-bezout ring and generalized // Applied Problems of Mechanics and Mathematics, 2011. Vol. 9.  pp. 69-73 (in Ukrainian).
  26. Zabavsky B.V., Vasyunyk I.S. Factorial analogue of the local quasi-duo domain // Matematychni Studii, -2011. -T.35, No 1. pp. 74-77 (in Ukrainian).
  27. Zabavsky B.V., Vasyunyk I.S. Rings of almost unit stable rank 1 // Ukrainian Mathematical Journal, -2011. Vol. 63, No. 6, pp. 840–843.
  28. Zabavsky B.V., Domsha O.V. Diagonalizability theorem for matrices over certain domains // Algebra and Discrete Mathematics, -2011. Vol. 12, No 1. pp. 132 – 139.
  29. Zabavsky B.V., Domsha O.V. Kazimirsky’s rings // Matematychni Studii, -2010. -T.34, No 1. pp. 75-79 (in Ukrainian).
  30. Zabavsky B.V., Domsha O.V. 2-Simple ore domains of stable rank 1 // Ukrainian Mathematical Journal, -2010. Vol. 62, No. 10, pp. 1436–1440.
  31. Zabavsky B.V., Domsha O.V. Block-diagonal reduction of matrices over an n-simple Bézout domain (n ≥ 3) // Ukrainian Mathematical Journal, -2010. Vol. 62, No. 2, pp. 275–280.
  32. Zabavsky B.V. Regular rings with an idempotent diagonal reduction of matrices // Visnyk Lviv Univ., 2009. Vol. 71.  pp. 102-105 (in Ukrainian).
  33. Zabavsky B.V. Fractionally regular Bezout rings // Matematychni Studii, -2009. -T.32, No 1. pp. 76-80.
  34. Zabavsky B.V., Petrychkovych V.M. On the stable range of matrix rings // Ukrainian Mathematical Journal, -2009. Vol. 61, No. 11, pp. 1575–1578.
  35. Zabavsky B.V., Kysil' T.N The right Bezout ring with completely prime Jacobson radical // Visnyk Lviv Univ., 2008. Vol. 68.  pp. 104-106 (in Ukrainian).
  36. Zabavsky B.V., Komarnytsky M.Ya. Cohen type theorem for adequateness and elementary divisor rings // Mathematical Methods and Physicomechanical Fields, -2008. -51, No 4. pp. 94-98 (in Ukrainian)
  37. Zabavsky B.V. Reduction of matrices over 3-simple Bezout domain // Visnyk Lviv Univ., 2008. Vol. 68.  pp. 97-103 (in Ukrainian).
  38. Zabavsky B.V., Romaniv O.M. Noncommutative n-elementary rings // Matematychni Studii, -2007. -T.27, No 1. pp. 95-99 (in Ukrainian).
  39. Zabavsky B.V., Kysil' T.N. Nearly simple elementary divisor domains // Bul. Acad. Ştiinţe Repub. Mold. Mat., -2006, No. 3, pp. 121-123.
  40. Zabavsky B.V. Almost atomic elementary divisor domains with stable range one // Matematychni Studii, -2006. -T.26, N 2. -212-216.
  41. Zabavsky B.V. Diagonalizability theorems for matrices over rings with finite stable range // Algebra and Discrete Mathematics, -2005. No 1. pp. 151-165.
  42. Zabavsky B.V. Diagonalization of matrices // Matematychni studii, -2005. -T.23, N 1. -3-10.
  43. Zabavsky B.V. Reduction of matrices and simultaneous diagonalization of pair of matrices over rings // Matematychni studii, -2005. -T.24, N 2. -3-11. (in Ukrainian).
  44. Zabavsky B.V. Simple elementary divisor rings // Matematychni studii, -2004. -T.22, N 2. -129-133 (in Russian)
  45. Zabavsky B.V., Gatalevich A.I. Symmetry of divisibility in elementary divisor ring // Visnyk Lviv Univ., 2004. Vol. 63.  pp. 77-79 (in Ukrainian).
  46. Zabavsky B.V. Diagonalization of matrices over ring with finite stable rank // Visnyk Lviv Univ., 2003, Vol. 61, pp. 206-210.
  47. Zabavsky B.V. Reduction of matrices over Bezout rings of stable rank not higher than 2 // Ukr. mat. journal -2003. -55, N 4. -550-554.
  48. Zabavsky B.V. Elementary reduction of matrices over adequate domain // Matematychni Studii, -2002. -T.17, N 2. -115-116.
  49. Zabavsky B.V. Factorial analog of distributive Bezout domains // Ukr. mat. journal -2001. -53, N 11, -1564-1567.
  50. Zabavsky B.V., Romaniv O.M. Commutative 2-Euclidean rings // Matematychni studii, -2001. -T.15, N 2. -140-144. (in Ukrainian).
  51. Zabavsky B.V. Reduction of matrices over right Bezout rings with finite stable rank // Matematychni studii. -2001. -16, N 2. -115-116. (in Ukrainian).
  52. Zabavsky B.V., Gatalevich A.I. Maximal nonprincipal right ideals of Bezout rings // Mathematical Methods and Physicomechanical Fields, -2000. -43, N 2. -40-44. (in Ukrainian).
  53. Zabavsky B.V., Romaniv O.M. Rings with Elementary Reduction of Matrices // Ukr. mat. journal, 2000. Vol. 52, No. 12, pp. 1641 – 1649. (in Ukrainian).
  54. Zabavsky B.V., Romaniv O.M. Noncommutative domains with elementary reduction of matrices // Mathematical Methods and Physicomechanical Fields, -1999. -42. -N4. -133-137. (in Ukrainian)
  55. Zabavsky B.V., Gatalevich A.I. On minimal prime ideals of commutative Bezout rings // Ukrainian Mathematical Journal, July 1999, Volume 51, Issue 7, pp 1129-1134
  56. Zabavsky B.V., Gatalevich A.I. Noncommutative elementary divisor rings // Journal of Mathematical Sciences, August 1999, Volume 96, Issue 2, pp 3013-3016
  57. Zabavsky B.V., Romaniv O.M. Any semilocal Bezout ring is a ring with elementary reduction of matrices // Matematychni Studii, 9 (1998) pp 3-6 (in Ukrainian)
  58. Zabavsky B.V. Rings over which every matrix admits the diagonal reduction by elementary transformations // Matematychni Studii, 8 (1997) pp 136-139 (in Ukrainian)
  59. Zabavskii B.V. Generalized adequate rings // Ukrainian Mathematical Journal, 1996, Volume 48, Issue 4, pp 614-617
  60. Zabavskii B.V. A noncommutattve analog of the Cohen theorem // Ukrainian Mathematical Journal, May 1996, Volume 48, Issue 5, pp 790-794
  61. Zabavsky B.V. On the commutative elementary divisors rings with finite number of minimal prime ideals // Algebra i Topologiya, Lviv, LDU, -1996. -74-79 (in Ukrainian)
  62. Zabavsky B.V. Strongly factorial elements of commutative domains // Journal of Soviet Mathematics, 1993, Volume 66, Issue 1, pp 2034-2035
  63. Zabavsky B.V. On PP-quasi-duo elementary divisors ring // Algebra i topologiya, Kiev, ISDO, -1993, -40-49. (in Ukrainian)
  64. Zabavsky B.V. On prime unity regular rings of elementary divisors // Math. Stud. 2 (1993) pp 21-22 (in Ukrainian)
  65. Zabavsky B.V. On commutative elementary divisor rings (in Ukrainian) // Visnyk Lviv Univ., 1990, Vol. 34, pp 51-53
  66. Zabavsky B.V., Komarnytsky M.Ya. Some properties of maximal and prime ideals of commutative Bezout domains (in Ukrainian) // Visnyk Lviv Univ., 1990, Vol. 34, pp 53-56
  67. Zabavsky B.V. On noncommutative rings with elementary divisors (in Russian) // Ukrainian Mathematical Journal, 1990, Vol. 42, No 6, pp 748-750
  68. Zabavsky B.V.,Komarnytskii M.Ya. Distributive elementary divisor domains // Ukrainian Mathematical Journal, 1990, Vol. 42, No 7, pp 890-892
  69. Zabavsky B.V. The strict factorial property and the factorial Jacobson radical (in Russian) // Matematiceskie issledovanija, 1990, Vol. 118, pp 36-41
  70. Zabavsky B.V., Komarnytsky M.Ya. On adequate rings // Visnyk Lviv Univ., 1988,  pp 39-43 (in Ukrainian)
  71. Zabavsky B.V. Strictly factorial elements in commutative domains // Mat. metody i fiz.-mech. polya, -1987. -26. -16-18. (in Russian)
  72. Zabavsky B.V. Noncommutative elementary divisor rings // Ukrainian Mathematical Journal, 1987, Vol. 39, No. 4, pp. 440–444
  73. Zabavsky B.V. Factorial elements of commutative Bezout domain // Mathematical Methods and Physicomechanical Fields, -1985. -22. -32-34. (in Russian)
  74. Zabavsky B.V., Kazimirskii P. S. Reduction of a pair of matrices over an adequate ring to a special triangular form by means of the same one-sided transformations // Ukrainian Mathematical Journal, 1984, Vol. 36, No 2, pp. 256-258
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