A semiring is uniserial if its ideals are totally ordered by inclusion. First, we show that a
semiring S is uniserial if and only if the matrix semiring M n (S) is uniserial. As a …

A domain R is called conducive if every conductor ideal (R: T) is nonzero for all overrings T
of R other than the quotient field of R. Let H denote the set of all commutative rings R for …

Let R be a commutative ring with identity and N be a submodule of an R-module M. We say
a nonnil submodule N of an R-module M is a Φ-powerful (resp., Φ-strongly prime) …

Let ℋ be the set of all commutative rings with unity whose nilradical is a divided prime ideal.
The concept of maximal non-nonnil-PIR is introduced to generalize the concept of maximal …