Reduction of matrices over Bezout rings and related problems of the theory of rings and modules

Speaker

Andriy Gatalevych

Associate Professor
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

When & where:

May 17, 2022 at 1500, room 709
3-b Naukova Str., Lviv, Algebra Department
Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine

Abstract of talk

The report is devoted to the study of diagonal reduction of matrices over different classes of Bezout rings of finite stable range. In terms of K-theory, the conditions are indicated when an arbitrary commutative Bezout domain is an elementary divisor ring. Semihereditary Bezout rings of Gelfand range 1 are investigated. The known theorems for Bezout rings of finite Krull dimension are generalized. The results are also obtained for the case of noncommutative Bezout rings, which are related to the structural properties of the rings.
It has been proved that the commutative Bezout domain in which an arbitrary nonzero prime ideal is contained in the unique maximal ideal, is an elementary divisor ring. The notion of stable range indicates the conditions when an arbitrary commutative Bezout domain is an elementary divisor ring.

Andriy Gatalevych
March 1, 2022

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On the second and weakly-second spectrum of a module

Speaker

Marta Maloid-Glebova

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

When & where:

November 30, 2021 at 1500,
online Zoom

Join Zoom Meeting:

https://us04web.zoom.us/j/739…
Meeting ID: 739 806 9872
Passcode: AUpYx5

Abstract of talk

In this talk, we study second modules over associative rings and give some basic properties of this concept. Also we define the notion of weakly-second submodule of a module over an arbitrary ring and study some relationships between second spectrum and weakly-second spectrum of a module.

Marta Maloid-Glebova
November 30, 2021

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

Speakers

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

When & where:

October 19, 2021 at 1500,

online Zoom

Join Zoom Meeting:

https://www.google.com/……
Meeting ID: 739 806 9872
Passcode: AUpYx5

Abstract of talk

In our reports, we will describe the structure of elements of the Zelisko group (the group of matrices which quasi-commuting with a given diagonal matrix) over a homomorphic image of a commutative Bezout domain of stable range 1.5.

Volodymyr Shchedryk
Victor Bovdi

October 19, 2021

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About the second spectrum of a multiplication module

Speaker

MARTA MALOID-GLEBOVA

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

When & where:

May 25, 2021 at 1500,
online Zoom

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Meeting ID: 739 806 9872
Passcode: AUpYx5

Abstract of talk

Let R be a associative ring and M an multiplicative R-module. Let Spec^s(M) be the the collection of all second submodules of M. In this talk, we consider a new topology on Spec^s(M), called the second classical Zariski topology, and investigate the interplay between the module theoretic properties of M and the topological properties of Spec^s(M). Moreover, we study Spec^s(M) from point of view of spectral space.

Marta Maloid-Glebova
May 25, 2021

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

Speakers

Vasyl’
Fedorchuk

Volodymyr
Fedorchuk

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

When & where

April 28, 2021 at 16:00
online Zoom

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Meeting ID: 739 806 9872
Passcode: AUpYx5

Abstract of talk

The classification of symmetry reductions for the Monge – Ampère equation in the space M(1,3) \times 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.

Vasyl’ Fedorchuk
Volodymyr Fedorchuk

April 28, 2021

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