according to the kidushin 2, a woman is acquired through money, a document, or marital relations. So if a man gives a womsn a diamond ring and they have marital relations, does that make her engaged to him? does she need to aquire a formal get to be able to marry someone else?
eti cohen, chicago,usa
Let us start by saying that questions such as these are among the heaviest and most serious questions in Jewish law. We are dealing with a question that can affect the progeny of this woman for all generations - not to mention serious potential violations of Jewish law. Therefore an actual Psak should only be rendered by one of the major Poskim of our generation.
That being said, let us offer a few simple guidelines. One of the basic requirements for Jewish marriage, regardless of how it is performed, is that two Kosher witnesses must witness the act of marriage. In this case, that means that they see the man give the woman the diamond ring, or perhaps they see the couple concealing themselves in a room for the purpose of marital relations. A Kosher witness is a Jewish man that is Torah observant. (It is possible that even if they did not witness either of the above acts, but they see the couple living together as man and wife, then there is a potential problem). Short of the above scenarios there is not much chance that this man and woman are married.
Kol Tuv,
Rabbi Yonasan Sigler