Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
Theorem. Let R a commutative Bezout domain and a is a nonzero element of R. Then R/aR is a semipotent ring iff for any b ∈ R such that b ∉ J(aR) there are noninvertible r,s ∈ R such that a=rs, rR+bR=R, rR+sR=R.