proregular

English

Etymology

pro- +‎ regular

Adjective

proregular (not comparable)

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

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