ascending chain condition,
n. the condition on submodules that no ascending chain
I1 ⊆ I2 ⊆ I3 ⊆...,
of which each member is contained in the next, has more than a finite number of distinct members; equivalent to the maximum condition that every non-empty set of submodules has a maximal element. See Noetherian module. Compare descending chain condition.
I1 ⊆ I2 ⊆ I3 ⊆...,
of which each member is contained in the next, has more than a finite number of distinct members; equivalent to the maximum condition that every non-empty set of submodules has a maximal element. See Noetherian module. Compare descending chain condition.