On the module of first and second order differentials of R?_k S

摘要

Let R and S be k-algebras with characteristic zero. Let Ω_k^1 (R?_k S) and Ω_k^2 (R?_k S) are first and second order universal differential modules over R?_k S, respectively. The main result of this paper asserts that in which cases Ω_k^1 (R?_k S) and Ω_k^2 (R?_k S) can be free modules by using symmetric derivation.