Frompro- +‎regular.

proregular (notcomparable)

1. (mathematics) Having the property that the inverse systems of theKoszul cohomologymodules satisfy theInverse limit#Mittag-Leffler condition.)
   • 2016, Liran Shaul, “Adic reduction to the diagonal and a relation between cofiniteness and derived completion”, inarXiv‎^[1]:

     Then adic reduction to the diagonal holds:${\displaystyle A{\otimes }_{A{\hat{\otimes }}_K^{L}A}^L(M{\hat{\otimes }}_K^{L}N)\cong M{\otimes }_A^{L}N}$. (2) Let${\displaystyle A}$ be a commutative ring, let${\displaystyle a\subseteq A}$ be a weaklyproregular ideal, let${\displaystyle M}$ be an${\displaystyle A}$-module, and assume that the${\displaystyle a}$-adic completion of${\displaystyle A}$ is noetherian (if${\displaystyle A}$ is noetherian, all these conditions are always satisfied).

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