Proregular
adj ·Rare ·Advanced level
Definitions
- 1 Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.) not-comparable
"Then adic reduction to the diagonal holds: A#92;otimes#123;L#125;#95;#123;A#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;A#125;(M#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;N)#92;congM#92;otimes#123;L#125;#95;AN. (2) Let A be a commutative ring, let a#92;subseteqA 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)."
Example
More examples"Then adic reduction to the diagonal holds: A#92;otimes#123;L#125;#95;#123;A#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;A#125;(M#92;hat#123;#92;otimes#125;#123;L#125;#95;#123;K#125;N)#92;congM#92;otimes#123;L#125;#95;AN. (2) Let A be a commutative ring, let a#92;subseteqA 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)."
Etymology
From pro- + regular.
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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.