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

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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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Comaximal factorization in a commutative Bezout ring

Speaker

Oleh Romaniv

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

When & where:

March 30, 2021 at 1500,
online Zoom

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Meeting ID: 739 806 9872
Passcode: AUpYx5

Abstract of talk

We study an analogue of unique factorization rings in the case of an elementary divisor domain.

Oleh Romaniv
March 30, 2021

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

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:

February 23, 2021 at 1500,

online Zoom

Join Zoom Meeting:

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

Abstract of talk

Solutions of a linear equation a= bx in a homomorphic image of a commutative Bezout domain of stable range 1.5 is developed. It is proved that the set of solutions of a solvable linear equation contains at least one solution that divides the rest, which is called a generating solution. Generating solutions are pairwise associates. Using this result, the structure of elements of the Zelisko group is investigated.

Volodymyr Shchedryk
Victor Bovdi

February 23, 2021

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