Dg-separable dg-extensions

Alexander Zimmermann

arXiv:2412.06526·math.RA·January 7, 2026

Dg-separable dg-extensions

Alexander Zimmermann

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TL;DR

This paper introduces and characterizes dg-separable dg-extensions, focusing on graded commutative dg-division algebras in odd characteristic, and explores splitting conditions of dg-module sequences.

Contribution

It provides a complete characterization of dg-separable dg-extensions and the splitting criteria for dg-modules over such extensions, especially in the case of graded commutative dg-division algebras.

Findings

01

Complete characterization of dg-separable dg-extensions

02

Splitting of dg-module sequences over dg-separable extensions

03

Characterization in graded commutative dg-division algebras in odd characteristic

Abstract

We define and characterise completely dg-separable dg-extensions $φ : (A, d_{A}) \to (B, d_{B})$ . 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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Taxonomy

TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras