Abstract
Given a commutative ring $R$, the determinant map $\text{det}_0\colon Rk_0(R)\to \text{Pic\,}(R)$ given by $[M]-[R^m]\mapsto\langle\wedge^mM\rangle $ is a homomorphism from the additive group of $Rk_0(R)$ to the multiplicative group $\text{Pic\,}(R)$. In this paper, some properties of the determinant map $\text{det}_0$ are given and some results in [{\bf5}] are extended.
Citation
Yin Fancheng. Zhu Xiaosheng. "The determinant maps and K 0." Rocky Mountain J. Math. 44 (1) 91 - 102, 2014. https://doi.org/10.1216/RMJ-2014-44-1-91
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