4 articles
Faithfully flat descent
Faithfully flat descent is a technique in algebra and algebraic geometry, developed by Grothendieck, for transferring properties from a faithfully flat extension back to the base.
Flat module
A flat module is one whose tensoring preserves exactness of sequences; Serre introduced flatness in his 1956 GAGA paper, and Grothendieck recognized its geometric significance.
Torsion (algebra)
Torsion in algebra is the property of a module element killed by a nonzero ring element; every finite abelian group is a torsion module over the integers.
Torsion-free module
A torsion-free module is a module over an integral domain in which no nonzero element is killed by a nonzero ring element, generalizing torsion-free abelian groups.