Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
A unit-central simple Bezout domain R with stable range 1 is an elementary divisor ring iff R is a field.
Let R be a ring with stable range 1. Then from the condition aR+bR=R it follows there exist element u∈ U(R) that Ra+Rbu=R.
A unit-central Bezout ring R with stable range 1 is an elementary divisor ring iff R is a duo-ring.