Graded Coherence of Certain Extensions of Graded Algebras

Abstract

Let $\k$ be a field, and let $A$ and $B$ be connected $\mathbb{N}$-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.

12 pages; submitted to a journal