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not every ideal in $\barℤ$ is finitely generated.

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hbghlyj Posted at 2023-2-8 06:51:12 |Read mode
Last edited by hbghlyj at 2023-2-26 01:39:00Show 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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2025-4-20 22:20 GMT+8

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