On the isomorphism of coneat-injective modules over commutative rings

It is well-known that the family of coneat-injective modules has many properties that resemble the classes of injective modules, pure-injective modules and RD-injective modules. Moreover, injective modules are coneat-injective which, in turn, are RD-injective and, finally, RD-injective modules are pure-injective. For injective (respectively, pure-injective, RD-injective) modules, two such modules which are isomorphic to submodules (respectively, pure submodules, relatively divisible submodules) of each other are isomorphic. Motivated by these results, this communication is devoted to demonstrating that two coneat-injective modules which are isomorphic to coneat submodules of each other are likewise isomorphic.