Compositions of $n$-homomorphisms

Darij Grinberg

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arXiv · 2604.13619

Compositions of $n$-homomorphisms

Darij Grinberg

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Abstract

We study $n$-homomorphisms in the sense of Khudaverdian--Voronov, but generalized to maps from arbitrary rings to arbitrary commutative rings. We show that the sum of an $n$-homomorphism and an $m$-homomorphism is an $\left( n+m\right) $-homomorphism, and that the composition of an $n$-homomorphism and an $m$-homomorphism is an $nm$-homomorphism. The proofs are entirely combinatorial.

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Darij Grinberg. 2026-04-15. Compositions of $n$-homomorphisms. https://arxiv.org/abs/2604.13619

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