K0 of a ring
= K0 of a ring
{c}
{title2=$K_0(A)$}
The <Grothendieck group> of finitely generated projective right $A$-modules under <direct sum>. An element is a formal difference $[P]-[Q]$. Equality of two positive classes means $P\oplus T\cong Q\oplus T$ for some projective $T$; adding a complement of $T$ converts this into an <isomorphism> after a common finite free summand. This stabilization criterion is essential in patching arguments.