#### Vol. 15, No. 1, 2021

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The cancellation of projective modules of rank 2 with a trivial determinant

### Tariq Syed

Vol. 15 (2021), No. 1, 109–140
##### Abstract

We study the cancellation property of projective modules of rank $2$ with a trivial determinant over Noetherian rings of dimension $\le 4$. If $R$ is a smooth affine algebra of dimension $4$ over an algebraically closed field $k$ such that $6\in {k}^{×}$, then we prove that stably free $R$-modules of rank $2$ are free if and only if a Hermitian $K$-theory group ${\stackrel{˜}{V}}_{SL}\left(R\right)$ is trivial.

##### Keywords
cancellation, projective module, stably free module, Vaserstein symbol
##### Mathematical Subject Classification 2010
Primary: 19A13
Secondary: 13C10, 14F42, 19G38