Graded coherence of certain extensions of graded algebras

Abstract

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

Keywords:

• Graded coherent algebras
• twisted tensor products

2010 Mathematics Subject Classification:

• 16S70
• 16W50

Acknowledgments

We thank Joseph Carroll and Andrew Conner for several useful conversations, and the anonymous referee for noting some simplifications that improved the paper.