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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

Rings almost clean range 1

Bogdan Zabavsky

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

 

Abstract:

We introduce the notion a ring of a clean range 1 and a ring almost clean range 1.

Theоrem 1. Commutative ring of stable range 1 is a ring of clean range 1

There is an example of a rings of clean range 1, which is not a rings of stable range 1

Theоrem 2. Commutative Bezout ring of stable range 2 is an elementary divisors ring iff it is a ring almost clean range 1

 

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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