Research Communication | Open Access
Volume 2020 | Communication ID 69 |

Construction of a strongly co-hopfian Abelian Which the torsion part isn't strongly co-hopfian

Seddik Abdelalim
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
08 January 2020
23 January 2020
10 March 2020

Abstract: An abelian group A is called strongly co-hopfian if for every endomorphism α of A the chain Im(α1) _⊇ Im(α2) _⊇ Im(α3) _⊇ Im(α1) _⊇……. is stationary. In this work we characterize some properties of the strongly co-hopfian abelian group. Then we show that the p-component of strongly co-hopfian abelian group is also strongly co-hopfian but for the torsion part we construct strongly co-hopfian abelian group whose the torsion part is not strongly co-hopfian. method.