Bohdan Zabavsky

(125 голосів)
Перегляди: 54330 разів

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

 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., Andriychuk V., Gatalevych A., Pigura O. General Algebra // - Lviv: LNU, 2018. - 186 pp. (in Ukrainian)
  2. Zabavsky B.V. Diagonal reduction of matrices over rings // Mathematical Studies, Monograph Series, volume XVI, VNTL Publishers, 2012. Lviv. 251 pp. (english, 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., Romaniv O., Kuznitska B., Hlova T. Comaximal factorization in a commutative Bezout ring, Alg. and Discrete Math., Volume 30, Number 1 (2020) 150–160, DOI: 10.12958/adm1203
  2. Zabavsky B., Romaniv O. and J-Noetherian Bezout domain which is not of stable range 1, Journal of Algebra and Its Applications Vol. 19, No. 10 (2020) 2050187 (8 pages)  doi: 10.1142/S021949882050187X
  3. Zabavsky B., Popadiuk O. Simple element of a Bezout domain // International mathematical conference dedicated to the 60th anniversary of the department of algebra and mathematical logic of Taras Shevchenko National University of Kyiv (Kyiv, Ukraine, July 14–17, 2020) 86.
  4. Zabavsky B., Domsha O., Romaniv O. Clear elements and clear rings // International mathematical conference dedicated to the 60th anniversary of the department of algebra and mathematical logic of Taras Shevchenko National University of Kyiv (Kyiv, Ukraine, July 14–17, 2020) 85.
  5. Zabavsky B., Romaniv A., Kysil T. Elementary reduction of matrices over rings of almost stable range 1 // Algebra and Discrete Mathematics, Volume 29 (2020), Number 2, pp. 271–276. DOI: http://dx.doi.org/10.12958/adm1211
  6. Zabavsky B., Romaniv O. Almost zip Bezout domain. Matematychni Studii 53, no.2 (2020) 115-118 doi.org/10.30970/ms.53.2.115-118
  7. Zabavsky B., Domsha O. and Romaniv O. Clear elements and clear rings, arXiv:2005.03387v1 [math.AC] 7 May 2020.
  8. Zabavsky B.V., Bovdi V. Reduction of matrices over simple Ore domains, Linear and Multilinear Algebra (2020)  doi:03081087.2020.1743632
  9. Zabavsky B.V., Romaniv O.M. A Bezout ring of stable range 2 which has square stable range 1, Communications in Algebra Volume 47, Issue 12 (2019) 5392-5397 doi.org/10.1080/00927872.2019.1623239
  10. Zabavsky B.V. Rings of dyadic range 1, Journal of Algebra and Its Applications Vol. 18, No. 11 (2019) 1950206 (8 pages). doi.org/10.1142/S0219498819502062
  11. Zabavsky B.V., Bovdi V. Reduction of matrices over simple Ore domains, arXiv:1908.04545v1 [math.RA] 13 Aug 2019.
  12. Zabavsky B.V., Romaniv O.M. Rings with the Kazimirsky condition and rings with projective socle, Matematychni Studii 51, no.2 (2019) 124-129 (doi:10.15330/ms.51.2.124-129)
  13. Zabavsky B.V., Romaniv O.M. Diagonal reduction of matrices over Bezout rings of stable range 1 with the Kazimirsky condition, arXiv:1903.10049v1 [math.RA] 24 Mar 2019.
  14. Zabavsky B.V., Romaniv O.M. Almost zip Bezout domain // arXiv:1903.02847 [math.RA] 7 Mar 2019.
  15. Zabavsky B.V. Bass stable range // The Algebra Seminar, Department of Algebra, Charles University, Prague, Czech Republic, April 26, 2019.
  16. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // The Algebra Seminar, Department of Algebra, Charles University, Prague, Czech Republic, April 26, 2019.
  17. Zabavsky B.V., Gatalevych A.I. Diagonal reduction of matrices over commutative semihereditary Bezout rings // Communications in Algebra 47, no. 4 (2019) 1785-1795 DOI: 10.1080/00927872.2018.1521419
  18. Zabavsky B.V., Romaniv A. M., Bilavska S. I. Adequate properties of the elements with almost stable range 1 of a commutative elementary divisor domain // Applied Problems of Mechanics and Mathematics, Volume 16 (2018) 33–35.
  19. Zabavsky B.V., Romaniv O.M. J-Noetherian Bezout domain which is not a ring of stable range 1 // arXiv:1812.11195v1 [math.RA] 28 Dec 2018.
  20. Zabavsky B.V., Romaniv O.M. Commutative Bezout domains in which any nonzero prime ideal is contained in a finite set of maximal ideals, Carpathian Math. Publ. 10, no.2 (2018) 402-407.
  21. Zabavsky B.V., Romaniv O.M. A Bezout ring of stable range 2 which has square stable range 1 // arXiv:1812.08819 [math.RA] 20 Dec 2018.
  22. Zabavsky B.V.Type conditions of stable range for identification of qualitative generalized classes of rings // Algebra and Discrete Mathematics, Volume 26 (2018), Number 1, pp. 144–152
  23. Zabavsky B.V., Oliynyk R., Domsha O. A local adequate ring is a ring of adequate range 1 // Visnyk of the Lviv Univ. Series Mech. Math. 2017. Issue 84. P. 58-61.
  24. Zabavsky B.V., Gatalevych A.I. Diagonal reduction of matrices over commutative semihereditary Bezout rings // arXiv:1803.07627v1 [math.RA] 20 Mar 2018.
  25. Zabavsky B.V., Bokhonko V.V. A criterion of elementary divisor domain for distributive domains // Algebra and Discrete Mathematics, -2017. Vol. 23, No 1. pp. 1-6.
  26. Zabavsky B.V. Rings of Dyadic range 1 // arXiv:1702.03441v1 [math.RA] 11 Feb 2017.
  27. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // Communications in Algebra,Vol. 45, No 9, 2017.
  28. Zabavsky B.V. Type conditions of stable range for identification of qualitative generalized classes of rings // arXiv:1508.07418v1 [math.RA] 19 Apr 2016.
  29. 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.
  30. Zabavsky B.V., Pihura O. Commutative morphic rings of stable range 2 // Proc. Intern. Geom. Center 2015 8(3-4), pp. 65-68
  31. Zabavsky B.V., Gatalevych A.I. New characterizations of commutative clean rings // Matematychni Studii, -2015. -V.44, No 2. pp. 115-118.
  32. Zabavsky B.V., Pihura O. Gelfand local Bezout domains are elementary divisor rings // Carpathian Math. Publ. 2015, 7 (2), pp. 188–190.
  33. Zabavsky B.V., Pihura O. A morphic ring of neat range one // Algebra and Discrete Mathematics, -2015. Vol. 20, No 2. pp. 325-329.
  34. 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.
  35. Zabavsky B.V. Conditions for stable range of an elementary divisor rings // arXiv:1508.07418v1 [math.RA] 29 Aug 2015.
  36. 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.
  37. Zabavsky B.V., Kuznitska B.M. Avoidable rings  (Ukrainian, English) // Matematychni Studii, -2015. -V.43, No 2. pp. 153-155.
  38. Zabavsky B.V., Pihura O. Bezout morphic rings // Visnyk of the Lviv Univ. Series Mech. Math. 2014. Issue 79. P. 163-168
  39. 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.
  40. Zabavsky B.V., Kuznitska B.M. Effective ring // Algebra and Discrete Mathematics, -2014. Vol. 18, No 1. pp. 151-158.
  41. 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).
  42. 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.
  43. Zabavsky B.V. Diagonal reduction of matrices over finite stable range rings // Matematychni Studii, -2014. -V.41, No 1. pp. 101-108.
  44. 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
  45. 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)
  46. 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).
  47. 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.
  48. 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).
  49. 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.
  50. 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).
  51. 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).
  52. Zabavsky B.V., Vasyunyk I.S. Rings of almost unit stable rank 1 // Ukrainian Mathematical Journal, -2011. Vol. 63, No. 6, pp. 840–843.
  53. 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.
  54. Zabavsky B.V., Domsha O.V. Kazimirsky’s rings // Matematychni Studii, -2010. -T.34, No 1. pp. 75-79 (in Ukrainian).
  55. 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.
  56. 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.
  57. Zabavsky B.V. Regular rings with an idempotent diagonal reduction of matrices // Visnyk Lviv Univ., 2009. Vol. 71.  pp. 102-105 (in Ukrainian).
  58. Zabavsky B.V. Fractionally regular Bezout rings // Matematychni Studii, -2009. -T.32, No 1. pp. 76-80.
  59. Zabavsky B.V., Petrychkovych V.M. On the stable range of matrix rings // Ukrainian Mathematical Journal, -2009. Vol. 61, No. 11, pp. 1575–1578.
  60. 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).
  61. 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)
  62. Zabavsky B.V. Reduction of matrices over 3-simple Bezout domain // Visnyk Lviv Univ., 2008. Vol. 68.  pp. 97-103 (in Ukrainian).
  63. Zabavsky B.V., Romaniv O.M. Noncommutative n-elementary rings // Matematychni Studii, -2007. -T.27, No 1. pp. 95-99 (in Ukrainian).
  64. Zabavsky B.V., Kysil' T.N. Nearly simple elementary divisor domains // Bul. Acad. Ştiinţe Repub. Mold. Mat., -2006, No. 3, pp. 121-123.
  65. Zabavsky B.V. Almost atomic elementary divisor domains with stable range one // Matematychni Studii, -2006. -T.26, N 2. -212-216.
  66. Zabavsky B.V. Diagonalizability theorems for matrices over rings with finite stable range // Algebra and Discrete Mathematics, -2005. No 1. pp. 151-165.
  67. Zabavsky B.V. Diagonalization of matrices // Matematychni studii, -2005. -T.23, N 1. -3-10.
  68. 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).
  69. Zabavsky B.V. Simple elementary divisor rings // Matematychni studii, -2004. -T.22, N 2. -129-133 (in Russian)
  70. Zabavsky B.V., Gatalevich A.I. Symmetry of divisibility in elementary divisor ring // Visnyk Lviv Univ., 2004. Vol. 63.  pp. 77-79 (in Ukrainian).
  71. Zabavsky B.V. Diagonalization of matrices over ring with finite stable rank // Visnyk Lviv Univ., 2003, Vol. 61, pp. 206-210.
  72. 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.
  73. Zabavsky B.V. Elementary reduction of matrices over adequate domain // Matematychni Studii, -2002. -T.17, N 2. -115-116.
  74. Zabavsky B.V. Factorial analog of distributive Bezout domains // Ukr. mat. journal -2001. -53, N 11, -1564-1567.
  75. Zabavsky B.V., Romaniv O.M. Commutative 2-Euclidean rings // Matematychni studii, -2001. -T.15, N 2. -140-144. (in Ukrainian).
  76. Zabavsky B.V. Reduction of matrices over right Bezout rings with finite stable rank // Matematychni studii. -2001. -16, N 2. -115-116. (in Ukrainian).
  77. 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).
  78. 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).
  79. 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)
  80. 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
  81. Zabavsky B.V., Gatalevich A.I. Noncommutative elementary divisor rings // Journal of Mathematical Sciences, August 1999, Volume 96, Issue 2, pp 3013-3016
  82. 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)
  83. Zabavsky B.V. Rings over which every matrix admits the diagonal reduction by elementary transformations // Matematychni Studii, 8 (1997) pp 136-139 (in Ukrainian)
  84. Zabavskii B.V. Generalized adequate rings // Ukrainian Mathematical Journal, 1996, Volume 48, Issue 4, pp 614-617
  85. Zabavskii B.V. A noncommutattve analog of the Cohen theorem // Ukrainian Mathematical Journal, May 1996, Volume 48, Issue 5, pp 790-794
  86. 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)
  87. Zabavsky B.V. Strongly factorial elements of commutative domains // Journal of Soviet Mathematics, 1993, Volume 66, Issue 1, pp 2034-2035
  88. Zabavsky B.V. On PP-quasi-duo elementary divisors ring // Algebra i topologiya, Kiev, ISDO, -1993, -40-49. (in Ukrainian)
  89. Zabavsky B.V. On prime unity regular rings of elementary divisors // Math. Stud. 2 (1993) pp 21-22 (in Ukrainian)
  90. Zabavsky B.V. On commutative elementary divisor rings (in Ukrainian) // Visnyk Lviv Univ., 1990, Vol. 34, pp 51-53
  91. 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
  92. Zabavsky B.V. On noncommutative rings with elementary divisors (in Russian) // Ukrainian Mathematical Journal, 1990, Vol. 42, No 6, pp 748-750
  93. Zabavsky B.V.,Komarnytskii M.Ya. Distributive elementary divisor domains // Ukrainian Mathematical Journal, 1990, Vol. 42, No 7, pp 890-892
  94. Zabavsky B.V. The strict factorial property and the factorial Jacobson radical (in Russian) // Matematiceskie issledovanija, 1990, Vol. 118, pp 36-41
  95. Zabavsky B.V., Komarnytsky M.Ya. On adequate rings // Visnyk Lviv Univ., 1988,  pp 39-43 (in Ukrainian)
  96. Zabavsky B.V. Strictly factorial elements in commutative domains // Mat. metody i fiz.-mech. polya, -1987. -26. -16-18. (in Russian)
  97. Zabavsky B.V. Noncommutative elementary divisor rings // Ukrainian Mathematical Journal, 1987, Vol. 39, No. 4, pp. 440–444
  98. Zabavsky B.V. Factorial elements of commutative Bezout domain // Mathematical Methods and Physicomechanical Fields, -1985. -22. -32-34. (in Russian)
  99. 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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