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Journals / International Electronic Journal of Algebra / 2026 / Volume: 40 Issue: 40

Dg-separable dg-extensions

Alexander Zimmermann(Université de Picardie)
Pages
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Publication Date
2026-07-16
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We prove that for a dg-separable extension a short exact sequence of dg-modules over $(B,d_B)$ splits if and only if the restriction to $(A,d_A)$ splits.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We define and characterise completely dg-separable dg-extensions $\varphi\colon (A,d_A)\rightarrow(B,d_B)$.
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Key Findings & Data:We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$.
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Conclusion & Impact:We prove that for a dg-separable extension a short exact sequence of dg-modules over $(B,d_B)$ splits if and only if the restriction to $(A,d_A)$ splits.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Differential graded algebra · $~$ · $~~$

Abstract

We define and characterise completely dg-separable dg-extensions $\varphi\colon (A,d_A)\rightarrow(B,d_B)$. We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$. We prove that for a dg-separable extension a short exact sequence of dg-modules over $(B,d_B)$ splits if and only if the restriction to $(A,d_A)$ splits.

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Cite This Article

Zimmermann, A. (2026). Dg-separable dg-extensions. International Electronic Journal of Algebra, Volume: 40 Issue: 40. https://doi.org/10.24330/ieja.1924473

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