Expired Rings

I have a stock of puzzles intended for a contest that didn't happen. This one is the most obviously dated:

Write all digits from 0 to 9 on every ring. Any given clue is the result of addition, subtraction, multiplication, or exact division between the numbers to the immediate left and immediate right of the cell the clue is close to.

This was the final puzzle of the test, since I like tests to end on a high note for puzzlers rather than authors, and easier puzzles make hitting that note easier. This was also the last to be written, since I realised I was rather light on arithmetic content. Thanks to fantom for pointing out a typo in the original version.