Union Captains wear three golden rings on their lower sleves of Board and Dress Uniform Jackets. It used to be four rings until the foundation of the United Stars. Back then Terran Starship Captains wore 4 rings and sometimes the "Nelson loop" but since both Saran and Pan Saran Captains had a similar design with three rings it was decided to change it to three.
It is that way ever since.
Admirals have 4 or 5 rings.
No other rank or service has lower sleeve decoration.
The Rings of a Captain used to be made of Gold thread and called Captain's Gold.