I would say that dress ring is worth a second look. Although several manufacturers used ‘JG’ marks, that particular mark is not identified with 100% certainty but the consensus is that it’s probably the Jack Gutschneider Jewelry Co, of New York, NY. That’s my gut feeling too.
Gutschneider was a German-American designer and founded the company in 1957, initially using “Van Gogh” as a maker mark. He switched to “JG JLRY” and variations of it soon afterwards and there is no record of the company after 1963. If you compare the styling of the ‘J’ and the ‘G’ to the marks more commonly seen, I think there’s enough similarity to suggest it is his mark… perhaps used in abbreviated form on items too small to easily accommodate the mark in full.
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If it is by Gutschneider then it’s a highly collectable piece. He is known for modernist designs, many of his pieces are one-offs and he sold mainly to high-end jewellery stores. I wouldn’t worry about it being ‘only’ 10K. On a ring with a shank as thin as that, most jewellers would drop down in karats to get additional hardness. Also, if it is Gutschneider then it’s really unlikely that the stone is synthetic or cheap. From the colour I see, I suspect it may be an iolite and a nice one too.