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

Irwing Kaplansky

On finite homomorphic images of commutative Bezout domain

 

Bohdan Zabavsky

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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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

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