Graded coherence of certain extensions of graded algebras

摘要

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 -> 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.