| Autor: |
Abdelalim, Seddik, Chaïchaâ, Abdelhak, ElGarn, Mostafa |
| Zdroj: |
Ricerche di Matematica; Nov2024, Vol. 73 Issue 5, p2305-2319, 15p |
| Abstrakt: |
The characterization of automorphisms having the extension property in the category of modules is an open problem. In earlier works (Abdelalim et al. in: Springer proceedings in mathematics and statistics, vol 311, pp 313–323, 2020, Abdelalim et al. in Discuss Math-Gen Algebra Appl 43, 2023), the authors solved this problem in the category of direct sum of cyclic torsion-free modules over a BFD and in the category of a direct finite sum of cyclic modules with torsion over a UFD. It is natural to see what happens in other categories. In this paper, we extend the result in Abdelalim et al. (Discuss Math-Gen Algebra Appl 43, 2023) to the category of a direct infinite sum of cyclic modules over a BFD with torsions. Let A be a bounded factorization domain (BFD). Consider a direct infinite sum M of cyclic modules over A such that the torsion part of M is a proper submodule of M and let α be an automorphism of M. We give a necessary and sufficient condition such that α satisfies the extension property. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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