英和和英

形容詞

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: ${\displaystyle A\otimes _{A{\hat {\otimes }}_{K}^{L}A}^{L}(M{\hat {\otimes }}_{K}^{L}N)\cong M\otimes _{A}^{L}N}$. (2) Let ${\displaystyle A}$ be a commutative ring, let ${\displaystyle a\subseteq A}$ be a weakly proregular 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).