Menu

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

Irwing Kaplansky

A commutative morphic ring of stable range 2

 

 

Bogdan Zabavsky

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

 

 

Abstract:

 

It is know that a left quasi-morphic ring R is a ring of stable range 1 if and only if dim R=0.

(Developing Kaplansky ideas Canfell to introduced the concept of the set of principal ideals aiR, i=1,2,...,n, is uniquely generated of a commutative ring R, if whenever aiR=biR there exist elements uiє R such that ai=biui, i=1,2,...,n, such that ai=biui and u1R+u2R+...+unR=R. The dimension of a commutative ring R, denoted by dim R is the least integer n such that every set of n+1 principal ideals is unique generated.)

Theorem. A commutative morphic ring R is a ring of stable range 2 if and only if dim R=1.

 

References

Zabavsky B.V. Diagonal reduction of matrices over rings // Mathematical Studies, Monograph Series, volume XVI, VNTL Publishers, 2012. Lviv. 251 pp.

 

Коментарі (0)

Rated 0 out of 5 based on 0 voters
There are no comments posted here yet

Залиште свій коментар

Posting comment as a guest. Sign up or login to your account.
Вкладення (0 / 3)
Share Your Location
back to top
Bookmaker with best odds http://wbetting.co.uk review site.

links

links

contacts us

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

Photo gallery 2013