# On finite homomorphic images of commutative Bezout domain

- Written by Bohdan Zabavsky
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Professor

Department of Algebra and Logic

Faculty of Mechanics and Mathematics

Ivan Franko National University of L'viv

**Abstract:**

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.*

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