All rings are assumed to be associative and to have a nonzero identity element. Let A be a
ring, and let M be a right A-module. A proper ideal P of the ring A is said to be right primitive …

Let R be a commutative ring with identity and all modules are unital. Various generalizations
of primary ideals and primary modules have been studied. For example, a proper ideal I of R …

Let R be a ring with identity and let M be a unital left R-module. A proper submodule L of M
is radical if L is an intersection of prime submodules of M. Moreover, a submodule L of M is …

ABSTRACT A principal right ideal of a ring is called uniquely generated if any two elements
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …

For a ring A, the following conditions are equivalent. A is a right strongly semiprime ring.
Every right A-module which is injective with respect to some essential right ideal of the ring …

An extension ring S of a ring T is called a left quotient ring of T if for any two elements ΛH= 0
and y of S there exists an element a of T such that ax^ rO and ay belongs to T. Let R be a …

This paper was inspired by the work of Fuchs, Heinzer, and Olberding concerning primal
and completely irreducible ideals. It is proved that if R is a commutative Noetherian ring then …

Let R be a ring with identity. A unital left R-module M has the min-property provided the
simple submodules of M are independent. On the other hand a left R-module M has the …

Introduction: All rings in this paper are associative and have an identity. All modules will be
daitary. Let R be any ring and M a left R-module. A submodule N of M is called essential if …

It is shown that if every prime ideal minimal over an ideal I is finitely generated, then there
are only finitely many prime left ideals minimal over I. This immedeately generalizes Cohen's …