Session of the Lviv Algebraic Seminar dedicated to the memory of professorVasyl’ Ivanovych Andriychuk 

September 18, 2018 at 15:00 in Lecture Room 377 
Семінар присвячений 70літтю
від дня народження М. Я. Комарницького
On the least common multiple of matrices over
commutative principal ideal domains
Andriy RomanivDepartment of Algebra, Pidstryhach 



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 nonsingular matrices over a commutative principal ideal domain.
On Gao’s conjecture related with finite field high order elements
Roman Popovych Department of Specialized Computer Systems, 



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 Spolygons with annihilation conditions
Yuriy Ishchuk Department of Algebra and Logic 



November 21, 2017 at 15:05 in Lecture Room 377 
Abstract of talk
The notions of a semicommutative semigroup and an abelian polygon can be introduced by analogy with the notions of semicommutative, abelian modules and rings.
Semiscalar equivalence of third order polynomial matrices with only one characteristic root
Bogdan Shavarovskii Department of Algebra, Pidstryhach 



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
Vasyl’ Petrychkovych Department of Algebra, Pidstryhach 
Nataliia Dzhaliuk Department of Algebra, Pidstryhach 



October 17, 2017 at 15:05 in Lecture Room 377 
Abstract of talk
We consider matrix linear equations of form 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
Andriy Sagan Department of Algebra and Logic 



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 quasiEuclidean duoring being a ring with elementary matrix reduction. Using this criterion we will be able to describe various duorings with elementary matrix reduction. Moreover, it will be established that any right Hermite stable range one ring is a right Euclidean domain.