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OLEH ROMANIVDepartment of Algebra, Topology and Fundamental Mathematics |
March 30, 2021 at 15:00 onlineJoin Zoom Meeting |
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Abstract of talk
We study an analogue of unique factorization rings in the case of an elementary divisor domain.
A generating solution of a linear equation and structure of elements of the Zelisko group
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Volodymyr ShchedrykDepartment of Algebra, Pidstryhach |
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Victor BovdiUnited Arab Emirates University, |
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February 23, 2021 at 15:00 onlineJoin Zoom Meeting |
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Abstract of talk
Solutions of a linear equation 
in a homomorphic image of a commutative Bezout domain of stable range 1.5 is developed.
It is proved that the set of solutions of a solvable linear equation contains at least one solution that divides the rest, which is
called a generating solution. Generating solutions are pairwise associates. Using this result, the structure of elements of the
Zelisko group is investigated.
Adequate elements and domains which is not of stable range 1
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OLEH ROMANIVDepartment of Algebra, Topology and Fundamental Mathematics |
December 24, 2020 at 12:00 onlineJoin Zoom Meeting |
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Abstract of talk
Let R be a J-Noetherian Bezout domain which is not a ring of stable range 1. Then in R there exists a nonunit adequate element.
On adequacy of full matrices over adequate rings
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Andrii GatalevychDepartment of Higher Mathematics |
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Volodymyr ShchedrykDepartment of Algebra, Pidstryhach |
November 27, 2020 at 16:00 onlineJoin Zoom Meeting |
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Abstract of talk
The set of full matrices (i.e., matrices whose elements are relatively prime) of the second order over an adequate ring R is investigated. The concept of an adequate element in non-commutative rings is introduced. It is proved that nonsingular full second order matrices are right (left) adequate elements in the ring of second order matrices over R.
With deep regret we report that on August 1, 2020 suddenly passed away
supervisor of our seminar, Honored Professor of the Ivan Franko University of Lviv,
Doctor of Sciences in Physics and Mathematics, Head of the Department of Algebra and Logic,
a famous scientist and talented teacher
prof. Bogdan V. Zabavsky
(19.08.1957 − 01.08.2020)
We express our deep and sincere condolences to his family and friends,
employees of the Department of Algebra and Logic, students.
Our memory of prof. Bogdan V. Zabavsky will never die.
AAA
On the semiscalar equivalence of 3-by-3 matrices with all different characteristic roots
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Bogdan ShavarovskiiDepartment of Algebra, Pidstryhach |
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October 15, 2019 at 15:05 in Lecture Room 377 |
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Abstract of talk
Some invariants of 3-by-3 polynomial matrices with all different characteristic roots are found. In some cases, the conditions of semiscalar equivalence of such matrices are specified and canonical forms are constructed.
Equivalence of matrices over quadratic rings and matrix equations
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Natalija LadzoryshynDepartment of Algebra, Pidstryhach |
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September 24, 2019 at 15:05 in Lecture Room 377 |
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Abstract of talk
The notation of the 
-equivalence of matrices over quadratic rings is introduced. The standard forms of matrices and their pairs with respect to this equivalence are established. The conditions of solvability of matrix linear unilateral and bilateral equations over an arbitrary quadratic ring are given and their integer solutions are described. On the basis of constructed standard forms of matrices, we proposed the effective method of solvability of these matrix equations and description of the structure of their solutions.
-equivalence of matrices over quadratic rings is introduced. The standard forms of matrices and their pairs with respect to this equivalence are established. The conditions of solvability of matrix linear unilateral and bilateral equations over an arbitrary quadratic ring are given and their integer solutions are described. On the basis of constructed standard forms of matrices, we proposed the effective method of solvability of these matrix equations and description of the structure of their solutions.Equivalence and factorization of the Kronecker products of polynomial matrices
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Volodymyr ZeliskoDepartment of Algebra and Logic |
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April 16, 2019 at 15:05 in Lecture Room 377 |
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Abstract of talk
We consider the problem of equivalence and semiscalar equivalence of the Kronecker products of polynomial matrices and their separation of factors.