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Results tagged with artin-ring
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user 75735
Questions about rings satisfying the descending chain condition on ideals.
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commutative, infinite, artinian ring (with unity) in which distinct ideals has distinct index
Let $R$ be an infinite, commutative, Artinian ring with the distinct-index property for distinct ideals. The claim is that $R$ is a field.
Case 1. $R$ has a nonzero ideal $I$ such that $I^2=0$.
Reas …
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