Why diethyl ether does not absorb in UV region?
We can measure the UV-Vis spectra for π → π* or n → π* electronic transitions (other transitions are forbidden according to selection rule) [1, pp. 577–578]. But in diethyl ether, being a saturated compound, it has no π-bonds. This successfully dismisses the idea of having π* orbital. And, as there is no π* orbital, we can not have a transition to the π* orbital resulting in no UV-Vis absorption spectra.
Reference

Pavia, D. L.; Lampman, G. M.; Kriz, G. S.; Vyvyan, J. R. Introduction to Spectroscopy, 5th ed.; Cengage Learning: Stamford, CT, 2015. ISBN 978-1-285-46012-3. (PDF)