Comparable overrings of a commutative ring

Abstract

Let H be the set of all commutative rings R such that Nil(R) is a divided prime ideal of R and let φ : T (R) → RNil(R) be a ring homomorphism defined as φ(x) = x for all x ∈ T (R). An overring Ro of an integral domain R is said to be comparable if Ro = R, Ro = qf(R), and each overring of R is comparable to Ro under inclusion. We study comparable overrings of a ring in class H.