Madonna has given the biggest sign yet that she and Alex Rodriguez are an item - by introducing him to her close friends.

The singer held an intimate dinner party in her apartment for the baseball star and also invited along some of her non-Kaballah chums.

But the move has infuriated estranged husband Guy Ritchie because it featured a number of their mutual friends.

The 40-year-old is livid that Madonna, 50, is showing off A-Rod, 33, so soon after he and his wife announced their split.

A source said: "It is a massive slap in the face for Guy and he really finds the whole thing quite embarrassing.

"As you can imagine, both he and Madonna share a lot of mutual friends who they still keep in touch with.

"Guy found out through one of them about this party and was pretty p*****-off about the whole thing.

"He thought it showed a great deal of disrespect to him so soon after the announcement of their break up."

The party, which was held two weeks ago in New York, was attended by Madge's pal Ingrid Casares, who was guest of honour, and producer Victor Calderone. Guy was already fuming after A-Rod's friendship with Madonna was made public during the summer.

Despite the fact that he and Madonna had by then decided to split up, the film director and his wife kept up the pretence that they were still together.

The source added: "The flurry of stories over the summer were acutely embarrassing for Guy.

"He wanted to speak up and say that he and Madge were no longer together. But he was told, in no uncertain terms, that he had to wait until Madonna's tour was finished.

"In the end, the charade got too much anyway and Guy said it all had to end.

"As a result, there's no love lost between Guy and A-Rod and the thought of him being introduced to all their mutual friends is just too much."