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本帖最后由 hbghlyj 于 2023-2-26 01:39 编辑 Show that if $R$ is an integral domain in which every ideal is finitely generated then $R$ has the ACCP. Assuming that the algebraic integers, $\barℤ$, form a ring, show that it has no irreducible elements and deduce that not every ideal in $\barℤ$ is finitely generated. |
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