Singularities of the structure of two-sided ideals of a domain of elementary divisors
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.
KeywordsPrincipal Ideal Jacobson Radical Elementary Divisor Simple Ring Inverse Element
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