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March 2022 A note on pairs of rings with the same prime ideals
Rahul Kumar, Atul Gaur
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Hiroshima Math. J. 52(1): 103-112 (March 2022). DOI: 10.32917/h2021037


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.


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Rahul Kumar. Atul Gaur. "A note on pairs of rings with the same prime ideals." Hiroshima Math. J. 52 (1) 103 - 112, March 2022.


Received: 13 May 2021; Revised: 16 September 2021; Published: March 2022
First available in Project Euclid: 25 March 2022

Digital Object Identifier: 10.32917/h2021037

Primary: 13B99
Secondary: 13A15 , 13A18

Keywords: $\phi$-chained ring , $\phi$-PVR , Overring

Rights: Copyright © 2022 Hiroshima University, Mathematics Program


Vol.52 • No. 1 • March 2022
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