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