Abstract
We study the ring extensions $R \subseteq T$ having the same set of prime ideals provided $\mathrm{Nil}(R)$ 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.
Funding Statement
The first author is supported by the SRF grant from UGC India, Sr. No. 2061440976.
The Second author is supported by the MATRICS grant from DST-SERB, No. MTR/2018/ 000707.
Citation
Rahul Kumar. Atul Gaur. "A note on pairs of rings with the same prime ideals." Hiroshima Math. J. 52 (1) 103 - 112, March 2022. https://doi.org/10.32917/h2021037
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