A personal list.

- Hope the hypothetical author would not restrict the base to be a field, even perhaps allowing another DGA as base.  (Most of the following comments probably assume this.)
- The flatness hypotheses over the base and Shukla homology as a repair for this.  Invariance of Shukla homology under weak equivalences of DGAs.
- Relationship to Tor<sup>R&otimes;R<sup>op</sup></sup>(R,M).
- For R&rarr;S a map of commutative DGAs with S flat over R, the Hochschild homology spectral sequence starting with HH<sup>R</sup>(S, Tor<sup>R</sup>(M,N)) and converging to Tor<sup>S</sup>(M,N).
- Base-change formulas, ranging from simple ones to the following:
$$
S \otimes_{HH^R(S)}^{\mathbb L} HH^R(A,M) \simeq HH^S(A,M)
$$