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arXiv · 2001.03123

Graded Coherence of Certain Extensions of Graded Algebras

Peter Goetz
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Abstract

Let $\k$ be a field, and let $A$ and $B$ be connected $\N$-graded $\k$-algebras. The algebra $A$ is said to be a graded right-free extension of $B$ provided there is a surjective graded algebra morphism $\pi: A \to B$ such that $\ker\pi$ is free as a right $A$-module. Suppose that $B$ is graded left coherent, and that $A$ is a graded right-free extension of $B$. We characterize when $A$ is also graded left coherent. We apply our criterion to prove graded coherence of certain non-Noetherian graded twisted tensor products.

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Peter Goetz. 2020-01-09. Graded Coherence of Certain Extensions of Graded Algebras. https://doi.org/10.1080/00927872.2020.1775844

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