Abstract

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.

摘要

众所周知，coneat-injective 模块族具有许多类似于单射模块、纯单射模块和 RD-injective 模块的类的属性。此外，单射模块是连续内射的，而后者又是 RD-内射的，最后，RD-内射模块是纯内射的。对于内射（分别为纯内射、RD-内射）模块，两个这样的模块同构于彼此的子模块（分别为纯子模块、相对可分子模块）是同构的。受这些结果的启发，本次交流致力于证明与彼此的子模块同构的两个单内射模块同样是同构的。