Freeness of closed ideals in O_d via completed tensor products

Determine whether every closed right (respectively, left) ideal in O_d is free as a right (respectively, left) O_d-module in the sense of completed tensor products following Taylor’s framework.

Background

While O_d(R) is shown to be a semifir and finitely generated ideals are free, the paper prompts whether, in the global entire setting O_d, all closed ideals are free when module structure is interpreted via completed tensor products in the spirit of Taylor’s non-commutative functional calculus.

This extends classical Bezout-type structural questions to the NC entire-function setting with topological module considerations.