Category Archives: Fall 2020

Adequate elements and domains which is not of stable range 1

OLEH ROMANIV

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

December 24, 2020 at 12:00 online

Join Zoom Meeting
https://us04web.zoom.us/j/7398069872?pwd=dzV0TS9WcTIyMEZZYzlKVTdOWDZSUT09
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.

AAA

On adequacy of full matrices over adequate rings

Andrii Gatalevych

Department of Higher Mathematics
Faculty of Mechanics and Mathematics
Ivan Franko
National University of L’viv

Volodymyr Shchedryk

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

November 27, 2020 at 16:00 online

Join Zoom Meeting
https://us04web.zoom.us/j/7398069872?pwd=dzV0TS9WcTIyMEZZYzlKVTdOWDZSUT09
Meeting ID: 739 806 9872
Passcode: 0UpYr5

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.

AAA