We prove that, in a domain of elementary divisors, the intersection of all nontrivial two-sided ideals is equal to zero. We also show that a Bézout domain with finitely many two-sided ideals is a domain of elementary divisors if and only if it is a 2-simple Bézout domain.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 6, pp. 854 – 856, June, 2010.
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Bilyavs’ka, S.I., Zabavs’kyi, B.V. Singularities of the structure of two-sided ideals of a domain of elementary divisors. Ukr Math J 62, 989–992 (2010). https://doi.org/10.1007/s11253-010-0406-7
- Principal Ideal
- Jacobson Radical
- Elementary Divisor
- Simple Ring
- Inverse Element