For a ring R, an R-module M is an abelian group with an R-action R×M→M satisfying distributivity and (rs)m = r(sm). Generalises vector spaces; homological algebra largely lives in modules.
For a ring R, an R-module M is an abelian group with an R-action R×M→M satisfying distributivity and (rs)m = r(sm). Generalises vector spaces; homological algebra largely lives in modules.