Category Archives: Spring 2017

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.

On the semigroup ID

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Anatolii Savchuk

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

 

April 04, 2017 at 15:05 in Lecture Room 377

Abstract of talk

There will be demonstrated some results, received in collaboration with O. Gutik and concerning the inverse semigroup ID_\infty of partially defined automorphisms of integers \mathbb{Z}.

In particular, the report includes the structural theorem for the semigroup ID_\infty.

On classification of low-dimensional Lie algebras

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Fedorchuk Vasyl’, Fedorchuk Volodymyr


Institute of Mathematics, Pedagogical University of Kraków, Poland;
Department of Algebra, Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics
National Academy of Sciences of Ukraine

 

March 21, 2017 at 15:05 in Lecture Room 372

Abstract of talk

We plan to present a short review of the results related to the classification of low-dimensional (\mathrm{dim}(L) \leq 4 )
Lie algebras.

Commutative Bezout domains whose non-trivial finite homomorphic images are semipotent rings

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Bohdan Zabavsky, Sofia Bilavska-Kudlata

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

 

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

Abstract of talk

In this talk we will investigate the structure of commutative Bezout domain whose non-trivial finite homorphic images are semipotent rings.