Let R be a commutative ring with unity. Let H denotes the set of all rings R such that Nil (R) is
a divided prime ideal. The notion of maximal non-Prüfer ring and maximal non-ϕ-Prüfer ring
is introduced which generalize the concept of maximal non-Prüfer subrings of a field. A
proper subring R of a ring S is said to be a maximal non-Prüfer subring of S if R is not a
Prüfer ring but every subring of S which contains R properly is a Prüfer ring. A proper
subring R of a ring S is said to be maximal non-ϕ-Prüfer subring of S if R is not a ϕ-Prüfer …

Let R be a commutative ring with unity. Let H denotes the set of all rings R such that Nil (R) is
a divided prime ideal. The notion of maximal non-Prüfer ring and maximal non-ϕ-Prüfer ring
is introduced which generalize the concept of maximal non-Prüfer subrings of a field. A
proper subring R of a ring S is said to be a maximal non-Prüfer subring of S if R is not a
Prüfer ring but every subring of S which contains R properly is a Prüfer ring. A proper
subring R of a ring S is said to be maximal non-ϕ-Prüfer subring of S if R is not a ϕ-Prüfer …