## The extension property in the category of direct sum of cyclic torsion-free modules over a BFD.(English)Zbl 1472.13034

Siles Molina, Mercedes (ed.) et al., Associative and non-associative algebras and applications. Proceedings of the 3rd Moroccan Andalusian meeting on algebras and their applications, MAMAA 2018, Chefchaouen, Morocco, April 12–14, 2018. Cham: Springer. Springer Proc. Math. Stat. 311, 313-323 (2020).
Let $$M$$ be a direct sum of cyclic torsion-free modules over an integral bounded factorization domain $$A$$. Let $$\alpha$$ be an automorphism of the $$A$$-module $$M$$. The aim of the paper is to show that $$\alpha$$ satisfies the extension property, i.e., for any monomorphism $$\lambda :M\rightarrow N$$ of $$A$$-modules, there exists an automorphism $$\overline{\alpha}$$ of $$N$$ such that $$\overline{\alpha}\lambda=\lambda \alpha$$, if and only if $$\alpha$$ is the multiplication by an invertible element of $$A$$.
For the entire collection see [Zbl 1433.16001].

### MSC:

 13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) 20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
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### References:

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