### Abstract

Let $B = A<X | dX=t >$ be an extended DG algebra by the adjunction of variable of positive even degree $n$, and let $N$ be a semi-free DG $B$-module that is assumed to be bounded below as a graded module. We prove in this paper that $N$ is liftable to $A$ if $Ext_B^{n+1}(N,N)=0$. Furthermore such a lifting is unique up to DG isomorphisms if $Ext_B^{n}(N,N)=0$.

Original language | Undefined/Unknown |
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Journal | arXiv |

Publication status | Published - May 15 2018 |

### Keywords

- math.AC
- 13D07, 16E45