Property: linearly compact

Definition: Given any family of submodules $N_i$ of $M$ indexed by $I$, and elements $m_i$ indexed by the same set, if $\bigcap_{i\in F}(m_i+N_i)\neq \emptyset$ for every finite subset $F$ of $I$, then $\bigcap_{i\in I}(m_i+N_i)\neq \emptyset$. (In other words, every finitely-solvable system of congruence is solvable.)


  • D. Zelinsky. Linearly compact modules and rings. (1953) @ whole article


This property has the following metaproperties
  • passes to submodules
  • passes to quotients