A note on pairs of rings with the same prime ideals
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Date
2022-03
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Hiroshima University
Abstract
We study the ring extensions R⊆T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exists properly containing R. Using idealization theory, the examples are also discussed to strengthen the results.
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Keywords
Mathematics, ϕ-chained ring, ϕ-PVR, Overring