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

Join Zoom Meeting:

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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