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Keywords:
maximal non-$\phi $-Mori ring; maximal non-Mori ring; normal pair
maximal non-$\phi $-Mori ring; maximal non-Mori ring; normal pair
Summary:
Let $\mathcal {H}$ be the set of all commutative rings with unity whose nilradical is a divided prime ideal. The concept of maximal non-$\phi $-Mori subrings of a ring is introduced to generalize the concept of maximal non-Mori subrings of domain. A proper subring $R$ of a ring $T\in \mathcal {H}$ is called a maximal non-$\phi $-Mori subring if $R$ is not a $\phi $-Mori ring but each subring of $T$ properly containing $R$ is a $\phi $-Mori ring.
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