A note on pairs of rings with same prime ideals

math.AC

/ Authors

/ Abstract

We study the ring extensions R \subseteq 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 exist properly containing R. Using idealization theory, the examples are also discussed to strengthen the results.

A note on pairs of rings with same prime ideals

math.AC

/ Authors

Rahul Kumar, Atul Gaur

/ Abstract

We study the ring extensions R \subseteq 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 exist properly containing R. Using idealization theory, the examples are also discussed to strengthen the results.