DIRECT SUMS OF INFINITELY MANY KERNELS

Abstract

Let kappa be the class of all right R-modules that are kernels of nonzero homomorphisms phi : E-1 -> E-2 for some pair of indecomposable injective right R-modules Et, E2. In a previous paper, we completely characterized when two direct sums A(l) circle plus center dot center dot center dot circle plus A(n) and B-l circle plus center dot center dot center dot circle plus B-m of finitely many modules A(i) and Bi in K are isomorphic. Here we consider the case in which there are arbitrarily, possibly infinitely, many A(i) and B-j in kappa. In both the finite and the infinite case, the behaviour is very similar to that which occurs if we substitute the class kappa with the class u of all uniserial right R-modules (a module is uniserial when its lattice of submodules is linearly ordered).