Abstract
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.
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