In algebra, a free presentation of a module M over a commutative ring R is an exact sequence of R-modules: ⨁ i ∈ I R → f ⨁ j ∈ J R → g M → 0. {\displaystyle \bigoplus _{i\in I}R\ {\overset {f}{\to }}\ \bigoplus _{j\in J}R\ {\overset {g}{\to }}\ M\to 0.} Note the image under g of the standard basis generates M. In particular, if J is finite, then M is a finitely generated module.
In algebra, a free presentation of a module M over a commutative ring R is an exact sequence of R-modules: ⨁ i ∈ I R → f ⨁ j ∈ J R → g M → 0. {\displaystyle \bigoplus _{i\in I}R\ {\overset {f}{\to }}\ \bigoplus _{j\in J}R\ {\overset {g}{\to }}\ M\to 0.} Note the image under g of the standard basis generates M. In particular, if J is finite, then M is a finitely generated module.
Source: Wikipedia "Free presentation" · CC BY-SA 4.0
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