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Andriy RomanivDepartment of Algebra, Pidstryhach |
March 27, 2018 at 15:05 in Lecture Room 377 |
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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.
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Roman PopovychDepartment of Specialized Computer Systems, |
December 5, 2017 at 15:05 in Lecture Room 377 |
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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.
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Yuriy IshchukDepartment of Algebra and Logic |
November 21, 2017 at 15:05 in Lecture Room 377 |
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The notions of a semi-commutative semigroup and an abelian 
-polygon can be introduced by analogy with the notions of semi-commutative, abelian modules and rings.
A semigroup is called a semi-commutative semigroup if for any 
implies 
. A right -polygon 
is called abelian if for any 
and any 
any idempotent 
Using the notions of Baer’s conditions for modules I will introduce p.p.-Baer -polygons and prove that if is a p.p.-Baer -polygon, then the conditions for to be a reduced, symmetric, semicommutative and an abelian -polygon are equivalent.
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Bogdan ShavarovskiiDepartment of Algebra, Pidstryhach |
November 7, 2017 at 15:05 in Lecture Room 377 |
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The canonical forms of polynomial matrices of the third order with only one characteristic root are established.
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Vasyl’ PetrychkovychDepartment of Algebra, Pidstryhach |
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Nataliia DzhaliukDepartment of Algebra, Pidstryhach |
October 17, 2017 at 15:05 in Lecture Room 377 |
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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.
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Andriy SaganDepartment of Algebra and Logic |
May 16, 2017 at 15:05 in Lecture Room 377 |
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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 
-Euclidean domain.
Additionally, it will be proved that for any pair of 
full matrices over elementary divisor ring, there exists a right (left) divisibility chain of length 
and over PID – of length 
Among the other results we will introduce the concept of e-atomic commutative ring and describe its main properties. Furthermore, we will show that any e-atomic Bezout domain and locally e-atomic Bezout ring are rings with elementary matrix reduction.
Finally, we will prove that a integral domain 
is an 
Euclidean ring if and only if a ring of formal Laurent series ![R [[ x,x^{-1}]]](http://unial.in.ua/wp-content/ql-cache/quicklatex.com-714491bc19c4aef71f1175f60975e6fe_l3.png "Rendered by QuickLaTeX.com")
is an Euclidean ring.
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Volodymyr ShchedrykDepartment of Algebra, Pidstryhach |
April 25, 2017 at 15:05 in Lecture Room 377 |
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We are going to describe the properties of polynomial matrix value on the system of matrix diagonal elements roots.
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Anatolii SavchukDepartment of Algebra and Logic |
April 04, 2017 at 15:05 in Lecture Room 377 |
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There will be demonstrated some results, received in collaboration with O. Gutik and concerning the inverse semigroup 
of partially defined automorphisms of integers 
.
In particular, the report includes the structural theorem for the semigroup .
