诱导丛的局部平凡性条件

The conditions for the induced bundle to be locally trivial

把由向量丛态射诱导出的三个特殊丛推广到模丛态射中,得到了相应的三个模丛:ker丛、im丛和coker丛;证明了如果两Z-模丛的纤维是可除的,则态射f诱导出的模丛imf和cokerf是局部平凡的;如果两模丛的纤维都是半单纯模,则三个诱导丛都是局部平凡的.最后,利用正合式将这些诱导丛联系起来.

Expand three especial induced vector bundles induced by a morphism of vector bundles to those induced by a morphism of module bundles so that three module bundles, ker bundles, im bundles and coker bundles are obtained. It is proved that if fibre of two Z-module bundles is divisible, then the module bundles imf and cokerf induced by a morphism f are locally trivial. When the fibres of two module bundle are semi-simplicial module, it is shown that three induced bundles, kerf, imf and cokerf are locally trivial. Lastly, by using exact sequences, some relations between kerf, imf and cokerf are given.