凝聚多项式扩张的Whitehead群(英文)

The Whitehead Groupof a Coherent Polynomial Extension

应用K1群的转化定理可以证明有限表现模范畴与有限生成投射模范畴的Whitehead群同构.从而可以证明一个正则稳定凝聚环与其上的多项式环的Whitehead群同构.作为推论,此结果对于广义伞环成立.

The resolution theorem for K1 implies that the whitehead groups of the categories of finitely presented modules and the categories of finitely generated projective modules over a coherent ring are isomorphic. From this it is obtained that the whitehead groups of a regular stably coherent ring R and the polynomial ring over R are isomorphic. As corollary, this result also holds for true any generalized umbrella ring R.