Decompositions of homomorphisms of abelian $p$-groups with $p^2$-bounded target

Stanisław Kasjan; Justyna Kosakowska

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arXiv · 2611.05156

Decompositions of homomorphisms of abelian $p$-groups with $p^2$-bounded target

Stanisław Kasjan·Justyna Kosakowska

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Abstract

Let $p$ be a prime. We classify homomorphisms $H:V_1\to V_2$ between abelian $p$-groups that are direct sums of cyclic groups, under the assumption $p^2V_2=0$. We prove that every such homomorphism is isomorphic to a direct sum of finite indecomposable representations and that this decomposition is unique up to isomorphism and reordering of the summands.

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BibTeX RIS

Stanisław Kasjan, Justyna Kosakowska. 2026-11-03. Decompositions of homomorphisms of abelian $p$-groups with $p^2$-bounded target. https://arxiv.org/abs/2611.05156

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