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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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