DOI: 10.3390/math14122215 ISSN: 2227-7390
Quillen–Suslin Theorem for Connected Cochain DG Algebras
Xuefeng Mao, Biyan ZhuLet A be a connected cochain differential graded algebra and P a finitely generated differential graded A-module. We show that P is semi-free if it is semi-projective and it is categorically free if it is categorically projective. It can be considered as a generalization of the well-known Quillen–Suslin Theorem in differential graded context. As an application, we show that the ghost length and the cone length of a compact differential graded module coincide.