Category Archives: Current semester

On the classification of symmetry reductions for the (1+3)-dimensional Monge-Ampère equation

Vasyl’Fedorchuk

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

 

April 28, 2021 at 16:00 online

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Abstract of talk

The classification of symmetry reductions for the Monge – Ampère equation in the space M(1,3) x R(u) is carried out. Some results obtained by using the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4) are presented.

Here: M(1,3) is the (1+3) – dimensional Minkowski space; R(u) is the real number axis of the dependent variable u.

AAA

Comaximal factorization in a commutative Bezout ring

OLEH ROMANIV

Department of Algebra, Topology and Fundamental Mathematics
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

March 30, 2021 at 15:00 online

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Abstract of talk

We study an analogue of unique factorization rings in the case of an elementary divisor domain.

AAA

A generating solution of a linear equation and structure of elements of the Zelisko group

Volodymyr Shchedryk

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

Victor Bovdi

United Arab Emirates University,
Al Ain, UAE

 

February 23, 2021 at 15:00 online

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Abstract of talk

Solutions of a linear equation a= bx 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.

AAA

Adequate elements and domains which is not of stable range 1

OLEH ROMANIV

Department of Algebra, Topology and Fundamental Mathematics
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

December 24, 2020 at 12:00 online

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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.

AAA

On adequacy of full matrices over adequate rings

Andrii Gatalevych

Department of Higher Mathematics
Faculty of Mechanics and Mathematics
Ivan Franko
National University of L’viv

Volodymyr Shchedryk

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

November 27, 2020 at 16:00 online

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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.

AAA

On the semiscalar equivalence of 3-by-3 matrices with all different characteristic roots

 

Bogdan Shavarovskii

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

 

October 15, 2019 at 15:05 in Lecture Room 377

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.

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Equivalence of matrices over quadratic rings and matrix equations

 

Natalija Ladzoryshyn

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

 

September 24, 2019 at 15:05 in Lecture Room 377

Abstract of talk

The notation of the (z,k)-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.

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