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"I liked the algebraic way of looking at things.
I’m additionally fascinated when the algebraic method is applied to infinite objects”.

Irwing Kaplansky

Stable range conditions for abelian and duo rings

Andry Gatalevych

Associate Professor
Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv

Anatolii Dmytruk

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv

 

Abstract:

We introduce the concepts of a ring of (von Neumann) regular range 1, a ring of semihereditary range 1, a ring of regular range 1. We find relationships between the introduced classes of rings and known ones for abelian and duo rings. We proved that Hermite duo ring of Gelfand range 1 is an elementary divisor ring.

 

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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at franko.lviv.ua

Scientific seminar, Aprill, 2015