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.

On Gao’s conjecture related with finite field high order elements

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Roman Popovych

Department of Specialized Computer Systems,
Lviv Polytechnic National University

 

December 5, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The talk will be devoted to the Gao’s conjecture connected with the construction of elements of provable high multiplicative order in general finite fields.

Semigroups and S-polygons with annihilation conditions

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Yuriy Ishchuk

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

 

November 21, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The notions of a semi-commutative semigroup and an abelian S-polygon can be introduced by analogy with the notions of semi-commutative, abelian modules and rings.

Semiscalar equivalence of third order polynomial matrices with only one characteristic root

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Bogdan Shavarovskii

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

 

November 7, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The canonical forms of polynomial matrices of the third order with only one characteristic root are established.

Matrix linear equations in two variables over rings

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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

 

October 17, 2017 at 15:05 in Lecture Room 377

Abstract of talk

We consider matrix linear equations of form AX+BY=C, AX+YB=C over commutative Bezout rings.
The goal is to present the method of solving such equations using the matrix pair standard form
with respect to generalized equivalence and to establish the particular solutions of the
equation, their construction method and the uniqueness criterion. Moreover, for certain classes of matrix equations
one can find their general solutions.

Matrix reduction over Bezout rings

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Andriy Sagan

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

 

May 16, 2017 at 15:05 in Lecture Room 377

Abstract of talk

It this talk the author will present main results of his PhD thesis.

We will discuss an elementary matrix reduction over different classes of commutative and noncommutative rings. In particular, we will specify the necessary and sufficient conditions for a quasi-Euclidean duo-ring being a ring with elementary matrix reduction. Using this criterion we will be able to describe various duo-rings with elementary matrix reduction. Moreover, it will be established that any right Hermite stable range one ring is a right \omega-Euclidean domain.

Matrix value on system of matrix diagonal elements roots and its properties

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Volodymyr Shchedryk

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

 

April 25, 2017 at 15:05 in Lecture Room 377

Abstract of talk

We are going to describe the properties of polynomial matrix value on the system of matrix diagonal elements roots.