Bohdan Zabavsky

zabavsky_photo Bohdan Volodymyrovych Zabavsky

Leader of seminar
Professor
Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

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

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. K-theoretical aspect of elementary divisor ring // 11-th International Algebraic Conference in Ukraine dedicated to the 75th anniversary of V.~V.~Kirichenko, Kyiv, Ukraine, 3-7 July 2017.
  2. Zabavsky B.V., Bokhonko V.V. A criterion of elementary divisor domain for distributive domains // Algebra and Discrete Mathematics. – 2017. – 23,№1. – P.1-6.
  3. Zabavsky B.V. Rings of Dyadic range 1 // arXiv:1702.03441v1 [math.RA] 11 Feb 2017.
  4. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // Communications in Algebra. – 2017. – Volume 45. – Issue 9. – p. 4062-4066
  5. Zabavsky B.V. Type conditions of stable range for identification of qualitative generalized classes of rings // arXiv:1508.07418v1 [math.RA] 19 Apr 2016.
  6. Zabavsky B.V., Bokhonko V.V. Canonical diagonal matrix reduction via invertible Toeplitz matrices // Bulletin of Donetsk National University. Series A. Natural Sciences. – 2015. – №1-2. – P. 7 – 11. (in Ukrainian)
  7. Zabavsky B.V., Pihura O. Commutative morphic rings of stable range 2 // Proc. Intern. Geom. Center 2015 8(3-4), pp. 65-68.
  8. Zabavsky B.V., Gatalevych A.I. New characterizations of commutative clean rings // Matematychni Studii, -2015. -V.44, No 2. pp. 115-118.
  9. Zabavsky B.V., Pihura O. Gelfand local Bezout domains are elementary divisor rings // Carpathian Math. Publ. 2015, 7 (2), pp. 188–190.
  10. Zabavsky B.V., Pihura O. A morphic ring of neat range one // Algebra and Discrete Mathematics, -2015. Vol. 20, No 2. pp. 325-329.
  11. Zabavsky B.V. K-theoretical aspect theory of the rings and modules // The common session of Department of mathematics NAS of Ukraine and mathematics and mathematical modelling section of West science center of NAS of Ukraine and MES of Ukraine dedicated to prof. P.S. Kazimirskii 90-th birth anniversary, Lviv, 23 October, 2015.
  12. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // arXiv:1508.07418v1 [math.RA] 29 Aug 2015.
  13. 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.
  14. Zabavsky B.V., Kuznitska B.M. Avoidable rings // Matematychni Studii, -2015. -V.43, No 2. pp. 153-155.
  15. Zabavsky B.V., Pihura O. Bezout morphic rings // Visnyk of the Lviv Univ. Series Mech. Math. 2014. Issue 79. pp. 163-168.
  16. 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.
  17. Zabavsky B.V., Kuznitska B.M. Effective ring // Algebra and Discrete Mathematics, -2014. Vol. 18, No 1. pp. 151-158.
  18. Zabavsky B.V., Kuznitska B.M. A stable range of class full matrices over elementary divisor ring // Ukrainian Mathematical Journal, -2014. Vol. 66, No. 5, pp. 697–700.
  19. Zabavsky B.V. A sharp Bezout domain is an elementary divisor ring // Ukrainian Mathematical Journal, -2014. Vol. 66, No. 2, pp. 284–288.
  20. Zabavsky B.V. Diagonal reduction of matrices over finite stable range rings // Matematychni Studii, -2014. -V.41, No 1. pp. 101-108.
  21. 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.
  22. Zabavsky B.V., Gatalevych A.I. Fractionally IF-Bezout ring // Visnyk of the Lviv Univ. Series Mech. Math. 2013. Issue 78. pp. 31–35. (in Ukrainian)
  23. Zabavsky B.V., Bilavska S.I. Decomposition of finitely generated projective modules over Bezout ring // Mat. Stud., -2013, Vol. 40, pp. 104–107.
  24. 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)
  25. 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.
  26. Zabavsky B.V., Bilavska S.I. Weak global dimension of finite homomorphic images of commutative Bezout domain // Applied Problems of Mechanics and Mathematics, -2012. Vol. 10, pp. 71-73. (in Ukrainian)
  27. Zabavsky B.V., Zelisko H.V., Kysil T. On right Bezout rings with finite stable range // Math. Bull. of the Shev. Sc. Soc., -2012, Vol.9, pp. 124-128. (in Ukrainian).
  28. 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.
  29. Zabavsky B.V., Bilavska S.I. On the structure of maximal non-finitely generated ideals of ring and Cohen’s theorem // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, -2011, Vol. 65, No. 1, pp. 33–41.
  30. Zabavsky B.V., Bilavska S.I. Every zero adequate ring is an exchange ring // Fundamentalnaya i Prikladnaya Matematika, -2011/2012, Vol. 17, No. 3, pp. 61–66.
  31. Zabavsky B.V., Vasyunyk I.S. Stable range adequate duo-bezout ring and its generalizations // Applied Problems of Mechanics and Mathematics, 2011. Vol. 9. pp. 69-73. (in Ukrainian)
  32. 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)
  33. Zabavsky B.V., Vasyunyk I.S. Rings of almost unit stable rank 1 // Ukrainian Mathematical Journal, -2011. Vol. 63, No. 6, pp. 840–843.
  34. 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.
  35. Zabavsky B.V., Domsha O.V. Kazimirsky’s rings // Matematychni Studii, -2010. -T.34, No 1. pp. 75-79. (in Ukrainian)
  36. Zabavsky B.V., Bilavska S.I. Singularities of the structure of two-sided ideals of elementary divisor domain // Ukrainian Mathematical Journal, -2010, Vol. 62, No. 6, pp. 854–856.
  37. Zabavsky B.V., Bilavska S.I. Stable rank of adequate ring // Mat. Stud. -2010, Vol. 33, pp. 212–214. (in Ukrainian)
  38. Zabavsky B.V., Bilavska S.I. Connection of adequate and clean rings // Applied Problems of Mechanics and Mathematics, -2010. Vol. 8, pp. 28-32. (in Ukrainian)
  39. 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.
  40. 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.
  41. Zabavsky B.V. Regular rings with an idempotent diagonal reduction of matrices // Visnyk Lviv Univ., 2009. Vol. 71. pp. 102-105. (in Ukrainian)
  42. Zabavsky B.V. Fractionally regular Bezout rings // Matematychni Studii, -2009. -T.32, No 1. pp. 76-80.
  43. Zabavsky B.V., Petrychkovych V.M. On the stable range of matrix rings // Ukrainian Mathematical Journal, -2009. Vol. 61, No. 11, pp. 1575–1578.
  44. 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)
  45. 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)
  46. Zabavsky B.V. Reduction of matrices over 3-simple Bezout domain // Visnyk Lviv Univ., 2008. Vol. 68. pp. 97-103. (in Ukrainian).
  47. Zabavsky B.V., Romaniv O.M. Noncommutative n-elementary rings // Matematychni Studii, -2007. -T.27, No 1. pp. 95-99. (in Ukrainian).
  48. Zabavsky B.V. Maximal nonprincipal ideals in Bezout domains // Applied Problems of Mechanics and Mathematics, -2006. Vol. 4., pp. 12-15. (in Ukrainian)
  49. Zabavsky B.V., Kysil’ T.N. Nearly simple elementary divisor domains // Bul. Acad. Ştiinţe Repub. Mold. Mat., -2006, No. 3, pp. 121-123.
  50. Zabavsky B.V. Almost atomic elementary divisor domains with stable range one // Matematychni Studii, -2006. -T.26, No 2. pp. 212-216.
  51. Zabavsky B.V. Diagonalizability theorems for matrices over rings with finite stable range // Algebra and Discrete Mathematics, -2005. No 1. pp. 151-165.
  52. Zabavsky B.V. Diagonalization of matrices // Matematychni studii, -2005. -T.23, No 1. pp. 3-10.
  53. Zabavsky B.V. Reduction of matrices and simultaneous diagonalization of pair of matrices over rings // Matematychni studii, -2005. -T.24, No 2. pp. 3-11. (in Ukrainian).
  54. Zabavsky B.V. Simple elementary divisor rings // Matematychni studii, -2004. -T.22, N 2. pp. 129-133. (in Russian)
  55. Zabavsky B.V., Gatalevich A.I. Symmetry of divisibility in elementary divisor ring // Visnyk Lviv Univ., 2004. Vol. 63. pp. 77-79. (in Ukrainian)
  56. Zabavsky B.V. Diagonalization of matrices over ring with finite stable rank // Visnyk Lviv Univ., 2003, Vol. 61, pp. 206-210.
  57. Zabavsky B.V. Reduction of matrices over Bezout rings of stable rank not higher than 2 // Ukr. mat. journal -2003. -55, N 4. pp. 550-554.
  58. Zabavsky B.V. Elementary reduction of matrices over adequate domain // Matematychni Studii, -2002. -T.17, N 2. pp. 115-116.
  59. Zabavsky B.V. Factorial analog of distributive Bezout domains // Ukr. mat. journal -2001. -53, No 11, pp. 1564-1567.
  60. Zabavsky B.V., Romaniv O.M. Commutative 2-Euclidean rings // Matematychni studii, -2001. -T.15, No 2. pp. 140-144. (in Ukrainian)
  61. Zabavsky B.V. Reduction of matrices over right Bezout rings with finite stable rank // Matematychni studii. -2001. -16, No 2. pp. 115-116. (in Ukrainian)
  62. Zabavsky B.V., Gatalevich A.I. Maximal nonprincipal right ideals of Bezout rings // Mathematical Methods and Physicomechanical Fields, -2000. -43, No 2. pp. 40-44. (in Ukrainian)
  63. 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)
  64. Zabavsky B.V., Romaniv O.M. Noncommutative domains with elementary reduction of matrices // Mathematical Methods and Physicomechanical Fields, -1999. -42. -No 4. pp. 133-137. (in Ukrainian)
  65. 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.
  66. Zabavsky B.V., Gatalevich A.I. Noncommutative elementary divisor rings // Journal of Mathematical Sciences, August 1999, Volume 96, Issue 2, pp. 3013-3016.
  67. 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)
  68. Zabavsky B.V. Rings over which every matrix admits the diagonal reduction by elementary transformations // Matematychni Studii, 8 (1997) pp. 136-139. (in Ukrainian)
  69. Zabavskii B.V. Generalized adequate rings // Ukrainian Mathematical Journal, 1996, Volume 48, Issue 4, pp. 614-617.
  70. Zabavskii B.V. A noncommutattve analog of the Cohen theorem // Ukrainian Mathematical Journal, May 1996, Volume 48, Issue 5, pp. 790-794.
  71. Zabavsky B.V. On the commutative elementary divisors rings with finite number of minimal prime ideals // Algebra i Topologiya, Lviv, LDU, -1996. pp. 74-79. (in Ukrainian)
  72. Zabavsky B.V. On PP-quasi-duo elementary divisors ring // Algebra i topologiya, Kiev, ISDO, -1993, pp. 40-49. (in Ukrainian)
  73. Zabavsky B.V. On simple unit-regular elementary divisor rings // Math. Stud. 2 (1993) pp. 21-22. (in Ukrainian)
  74. Zabavsky B.V. On commutative elementary divisor rings // Visnyk Lviv Univ., 1990, Vol. 34, pp. 51-53. (in Ukrainian)
  75. Zabavsky B.V., Komarnytsky M.Ya. Some properties of maximal and prime ideals of commutative Bezout domains // Visnyk Lviv Univ., 1990, Vol. 34, pp. 53-56. (in Ukrainian)
  76. Zabavsky B.V. On noncommutative rings with elementary divisors // Ukrainian Mathematical Journal, 1990, Vol. 42, No 6, pp. 748-750.
  77. Zabavsky B.V., Komarnytskii M.Ya. Distributive elementary divisor domains // Ukrainian Mathematical Journal, 1990, Vol. 42, No 7, pp. 890-892.
  78. Zabavsky B.V. The strict factorial property and the factorial Jacobson radical // Matematiceskie issledovanija, 1990, Vol. 118, pp. 36-41. (in Russian)
  79. Zabavsky B.V., Komarnytsky M.Ya. On adequate rings // Visnyk Lviv Univ., 1988, pp. 39-43. (in Ukrainian)
  80. Zabavsky B.V. Strictly factorial elements in commutative domains // Journal of Soviet Mathematics, 1993, Volume 66, Issue 1, pp. 2034-2035.
    Originally in Russian: Mat. metody i fiz.-mech. polya, -1987. -26. -16-18.
  81. Zabavsky B.V. Noncommutative elementary divisor rings // Ukrainian Mathematical Journal, 1987, Vol. 39, No. 4, pp. 440–444.
  82. Zabavsky B.V. Factorial elements of commutative Bezout domain // Mathematical Methods and Physicomechanical Fields, -1985. -22. pp. 32-34. (in Russian)
  83. 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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