Geodesic
The automorphisms having the extension property in a category of a finite direct sum of cyclic modules
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 111-120

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It is well known that the problem of characterizing the automorphisms, in the category of abelian groups, with the extension property is resolved [1]. But in other categories, it is a very difficult problem. This paper extends the result in [1] to a category of modules. Let A be a unique factorization integral domain (UFD). Consider M a direct finite sum of cyclic modules over A where A n n_A(M)={0} and α an automorphism of M. We give a necessary and sufficient condition such that α satisfies the extension property.
Keywords: integral domain, factorization, module, automorphism, torsion and torsion-free 
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Abdelalim, Seddik; Chaichaa, Abdelhak; El garn, Mostafa. The automorphisms having the extension property in a category of a finite direct sum of cyclic modules. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 111-120. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_1_a9/