Перегляд за автором "Zabavsky, B."

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  • A commutative Bezout PM* domain is an elementary divisor ring 
    Zabavsky, B.; Gatalevych, A. (Algebra and Discrete Mathematics, 2015)
    We prove that any commutative Bezout PM∗ domain is an elementary divisor ring.
  • A morphic ring of neat range one 
    Pihura, O.; Zabavsky, B. (Algebra and Discrete Mathematics, 2015)
    We show that a commutative ring R has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring R has a neat range one if and only if ...
  • Diagonalizability theorem for matrices over certain domains 
    Zabavsky, B.; Domsha, O. (Algebra and Discrete Mathematics, 2011)
    It is proved that R is a commutative adequate domain, then R is the domain of stable range 1 in localization in multiplicative closed set which corresponds s-torsion in the sense of Komarnitskii.
  • Diagonalizability theorems for matrices over rings with finite stable range 
    Zabavsky, B. (Algebra and Discrete Mathematics, 2005)
    We construct the theory of diagonalizability for matrices over Bezout ring with finite stable range. It is shown that every commutative Bezout ring with compact minimal prime spectrum is Hermite. It is also shown that a ...
  • Elementary reduction of matrices over rings of almost stable range 1 
    Zabavsky, B.; Romaniv, A.; Kysil, T. (Algebra and Discrete Mathematics, 2020)
    In this paper we consider elementary reduction of matrices over rings of almost stable range 1.