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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”.

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Adequate properties of the elements with almost stable range 1 of a commutative elementary divisor domain

 

Bohdan Zabavsky

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

 

Abstract:

Let R — commutative elementary divisor domain which is not a ring of stable range 1. Then exist element a∈R with almost stable range 1 (i.e. for any elements b,c∈R such that aR+bR+cR=R exist elements r that aR+(br+c)R=R). In this report we describe algebraic properties these elements r∈R. Lets note that a commutative elementary divisor domain of stable range 1 is 2-Euclidean domain of stable 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

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