DIRECT SUMS OF INFINITELY MANY KERNELS


Ecevit S., Facchini A., Kosan M. T.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.89, no.2, pp.199-214, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 89 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1017/s1446788710001539
  • Title of Journal : JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.199-214

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).