Embedding multi-wavelength lasers in photonic waveguide circuits is of interest for next-generation ion traps, such as for miniaturizing optical clocks or upscaling ion-based quantum computing. Critically, this path involves photonic integration of highly coherent lasers in the ultraviolet (UV) range, which is presently obstructed by the transparency limit of materials used in established integrated waveguides. Here, we demonstrate the first integrated, extended cavity diode laser based solely on UV-transparent materials. We integrate aluminum oxide waveguide circuits with gallium nitride amplifiers to generate milliwatt-level on-chip output power near the ultraviolet range. The extended cavity approach allows for wide wavelength coverage and precise frequency control, which is demonstrated by tuning mode-hop-free to a Sr-transition frequency. Due to the inherent stability of photonic circuits and UV-compatible integration, the intrinsic laser linewidth reaches a record-low value around 300 kHz with better than 43-dB side-mode suppression. These results announce the viability of a novel class of integrated lasers that opens access to the UV. Integrating UV lasers is of interest for portable optical clocks and ion-based quantum computers, but material absorption has impeded progress. Here, authors demonstrate a violet integrated laser using UV-transparent materials with mW-level output, narrow linewidth and precise frequency control.