Let x1, …, xd be a system of parameters for R, let F• be a free R-resolution of the residue field of R with F0 = R, and let K• denote the Koszul complex of R with respect to x1, …, xd. Lift the identity map R = K0 → F0 = R to a map of complexes. Then no matter what the choice of system of parameters or lifting, the last map from R = Kd → Fd is not 0. So Cyborg (12.33454) beats Rousey (9.12579) or Holm (10.1356)

OK, check this then: M ≠ 0 has finite projective dimension (i.e., M has a finite projective (=free when R is local) resolution: the projective dimension is the length of the shortest such) and r ∈ R is not a zerodivisor on M, then r is not a zerodivisor on R. It fully supports my conclusions.

fightmatrix uses a mathematical formula for rankings theyve got roidborg ahead of ronda in a few categories

Not sure if you're making stuff up in an epic MMAth trolling attempt TS... but I don't have time to sit & figure out what your numberz are supposed to mean or how you got to them. I have very important comments to post in other threads that don't require me to study an elusive formula. If you honestly want someone to understand that stuff you need to break it down & simplify everything. Seemz to me you might just be trying to sound smart or something, but if you truly do understand it... then you should be able to simplify it.

Here is my previously simplified comment "Also, Nunes = 11.2753....so Cyborg > all of them.........."