Hello Anon! The question of that ring has been addressed before, but it is worth doing again.
Mark Gatiss himself has answered this question through Twitter, and has said, categorically, that Mycroft is not married. In the United Kingdom, wedding rings are worn on the left hand, and Mycroft’s ring is worn exclusively on the right. Therefore, it is not a wedding ring.
Mycroft wears this ring throughout the series, and can be seen most prominently in Pink and Scandal. It is always worn on the ring finger of the right-hand and has been featured in several scenes. Its presence is as constant as his umbrella and his three-piece suit. It is also known to be a part of the Mycroft costume - although Mark Gatiss wears a similar ring on the same finger, he has stated that the ring seen in-series is a prop and is not his own.
Mark Gatiss has said he likes to think there’s a story behind the ring, which may be something that is revealed to us in time - I’m sure there will be a reason, otherwise he wouldn’t tease us so! That Anthea wears a similarly plain, gold band on the same finger when we see her in Pink, is extremely suggestive, but is by no means conclusive. It could also be something familial; it is not uncommon for a son to wear his late father’s ring. Or something else entirely.
Steven Moffat has joked that there is a laser in it, so its purpose really is open to interpretation!