In this note, we introduce a homological invariant for finitely generated modules over commutative noetherian local rings by slightly modifying the definition of complete intersection dimension defined by Avramov, Gasharov, and Peeva , and observe it from a relative point of view.
"Upper Complete Intersection Dimension Relative to a Local Homomorphism." Tokyo J. Math. 27 (1) 209 - 219, June 2004. https://doi.org/10.3836/tjm/1244208485