For {M_i}_(i element I) a family of R-modules indexed by a directed set I, let σ_(j i) :M_j->M_i i<=j be an R-module homomorphism. Call (M_i, σ_(j i)) an inverse system over I when 1.σ_(i i)(m) = m for all m element M_i. 2. When i<=j<=k, σ_(k i) = σ_(j i) °σ_(k j).

directed set | direct system | module | module homomorphism