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

Dg-separable dg-extensions

Alexander Zimmermann(Université de Picardie)
Sayfa
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Yayın Tarihi
2026-07-16
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez:We define and characterise completely dg-separable dg-extensions $\varphi\colon (A,d_A)\rightarrow(B,d_B)$.
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Temel Bulgular & Veri:We completely characterise the case of graded commutative dg-division algebras in characteristic different from $2$.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (17)

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