# Tagged Questions

**4**

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### $U\left(\mathfrak a\right) \otimes_{U\left(\mathfrak a\cap\mathfrak b\right)} U\left(\mathfrak b\right) \cong U\left(\mathfrak a + \mathfrak b\right)$ over a ring containing $\mathbb{Q}$

While the PoincarĂ©-Birkhoff-Witt theorem is usually proven (and sometimes even formulated) for free modules only, it is known (see also here) that it holds for arbitrary modules if the ground ring is ...

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### So, did Poincaré prove PBW or not?

This seems to be a question whose answer depends on whom you ask. Maybe we can come up with a final answer?
It is known that PoincarĂ©, at least, invented something that can be called ...