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

Join Zoom Meeting:

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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Adequate elements and domains which is not of stable range 1

Speaker

Oleh Romaniv

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

When & where:

Decemberar 24, 2020 at 1500,
online Zoom

Join Zoom Meeting:

Meeting ID: 739 806 9872
Passcode: AUpYx5

Abstract of talk

Let R be a J-Noetherian Bezout domain which is not a ring of stable range 1. Then in R there exists a nonunit adequate element.

Oleh Romaniv
December 24, 2020

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On adequacy of full matrices over adequate rings

Speakers

Volodymyr Shchedryk

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

Andrii
Gatalevych

Department of Higher Mathematics
Faculty of Mechanics and Mathematics Ivan Franko National University of Lviv

When & where:

November 27, 2020 at 1500,

online Zoom

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

Abstract of talk

The set of full matrices (i.e., matrices whose elements are relatively prime) of the second order over an adequate ring R is investigated. The concept of an adequate element in non-commutative rings is introduced. It is proved that nonsingular full second order matrices are right (left) adequate elements in the ring of second order matrices over R.

Volodymyr Shchedryk
Andriy Gatalevych

November 27, 2020

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Bohdan Zabavsky (19.08.1957 − 01.08.2020)

With deep regret we report that on August 1, 2020 suddenly passed away supervisor of our seminar, Honored Professor of the Ivan Franko University of Lviv, Doctor of Sciences in Physics and Mathematics, Head of the Department of Algebra and Logic, a famous scientist and talented teacher

prof. Bogdan V. Zabavsky

(19.08.1957 − 01.08.2020)

We express our deep and sincere condolences to his family and friends, employees of the Department of Algebra and Logic, students.

Our memory of prof. Bogdan V. Zabavsky will never die.