It is proved, among other results, that a prime right nonsingular ring (in particular, a simple
ring) R is right self-injective if RR is invariant under automorphisms of its injective hull. This …

A module is called automorphism-invariant if it is invariant under any automorphism of its
injective hull. In [Algebras for which every indecomposable right module is invariant in its …

In this paper, we provide the basic properties of (semi) simple hypermodules. We show that
if a hypermodule M is simple, then (E nd (M),·) is a group, where E nd (M) is the set of all …

Rings in which each finitely generated right ideal is automorphism-invariant (right fa-rings)
are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that …

In this paper, we study rings having the property that every right ideal is automorphism-
invariant. Such rings are called right a-rings. It is shown that (1) a right a-ring is a direct sum …

" The study of modules which are invariant under the action of certain subsets of the
endomorphism ring of their injective envelope can be drawn back to the pioneering work of …

In this paper, we introduce homological structure theory of semirings and CP-semirings—
semirings all of whose cyclic semimodules are projective. We completely describe …

We say that an R-module M is virtually semisimple if each submodule of M is isomorphic to a
direct summand of M. A nonzero indecomposable virtually semisimple module is then called …

A restricted artinian ring is a commutative ring with an identity in which every proper
homomorphic image is artinian. Cohen proved that a commutative ring R is restricted …

A poor module is one that is injective relative only to semisimple modules and a module is
maximally injective if its domain of injectivity is a coatom in the lattice of domains of injectivity …