The structure of block matrices. I. Factorizations in the rings of the block matrices

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Vasyl’ Petrychkovych

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

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Nataliia Dzhaliuk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine
 

March 12, 2019 at 15:05 in Lecture Room 377

Abstract of talk

We investigate equivalences, factorizations, and matrix unilateral and bilateral equations in the rings of the block matrices. In the first part, we consider factorizations of the block matrices, in particular, the block triangular and the block diagonal matrices over integral domains of finitely generated principal ideals. Conditions for existence and uniqueness up to the association of the factorizations in such rings are established.

The arithmetic of solutions of the equation A = BX

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Volodymyr Shchedryk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine
 

February 26, 2019 at 15:05 in Lecture Room 377

Abstract of talk

We describing the properties of g.c.d. and l.c.m. of matrix equation A = BX solutions over
commutative elementary divisor domain.

Elementary reduction of matrices over rings with almost stable range 1

Bohdan Zabavsky

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

Andriy Romaniv

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine
 

November 27, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In the talk we investigate the elementary reduction of matrices over rings with almost stable range 1.

Classification of Symmetry Reductions for the Eikonal Equation

Vasyl’Fedorchuk

Institute of Mathematics,
Pedagogical University of Kraków, Poland;
Department of Algebra,
Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics
of the NAS of Ukraine

Volodymyr Fedorchuk

Department of Algebra,
Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics
of the NAS of Ukraine
 

November 6, 2018 at 15:05 in Lecture Room 377

 

Abstract of talk

In the talk we present the results concerning the relationship between the structural properties of low-dimensional (dim L ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincare group P(1,4) and the properties of the reduced equations for the eikonal equation. To obtain those results, we have performed the classification of the invariants as well as of the ansatzes for the above mentioned subalgebras. We also present some classes of invariant solutions for the eikonal equation.

Reduced Triangular Form of Polynomial Matrices and Its Invariants

 

Bogdan Shavarovskii

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine
 

October 16, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In this report the semiscalar equivalence of polynomial matrices of three-order is
investigated. In particular, the systems of invariants of reduced matrices have been found.

Session dedicated to the memory of professor Vasyl’ Ivanovych Andriychuk 

 

Session of the Lviv Algebraic Seminar dedicated to the memory of professor 

Vasyl’ Ivanovych Andriychuk 

September 18, 2018 at 15:00 in Lecture Room 377

Program

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On the least common multiple of matrices over
commutative principal ideal domains

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Andriy Romaniv

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine
 

March 27, 2018 at 15:05 in Lecture Room 377

Abstract of talk

In the talk it will be shown how to find Smith normal form and transforming matrices of the least common multiply of arbitrary pair of non-singular matrices over a commutative principal ideal domain.