Notation in Serge Lang - Algebra In Serge Lang's Algebra on page 772 in the middle there is an expression of this form $$K(A(C))=Z[A(C)]/R(A(C))$$. I don't understand what $Z[A(C)]$ is supposed to mean. Thanks.

The $Z$ denotes the integers, and $[A(C)]$ the set of isomorphism classes of objects in $A(C)$. Then $Z[A(C)]$ is just the free abelian group with generators the elements of $[A(C)]$.