flat module
A module over a ring such that tensoring with it preserves exact sequences. Technical term in commutative algebra and algebraic geometry.
A flat module is a module for which tensoring preserves exact sequences.
Projective modules are a stronger notion: every projective module is flat, but not conversely. Flatness is a generalization that captures torsion-free-like behavior over commutative rings.
Faithfully flat modules are flat modules that also reflect exactness; they are used in descent theory.
Compound of 平坦 (flat, level) and 加群 (module). The term is a direct calque of the English 'flat module', where 'flat' refers to the geometric intuition of a module being 'spread out' without torsion.