Jada Pinkett Smith Admits to August Alsina Relationship, But ...

Jada Pinkett Smith admits she had a relationship with August Alsina, but takes issue with his claim Will Smith gave permission ... because she and Will say it wasn't necessary, at that time.

Jada and Will sat down for her "Red Table Talk" show which streamed Friday on Facebook and admitted Jada did, in fact, have an "entanglement" with August around 4 and a half years ago ... after Jada and Will had quietly separated. At the time, Jada said she thought the separation was going to be indefinite and didn't think Will was ever going to talk to her again.

In that time, Jada says she and August -- with whom the Smiths were good friends -- started dating. She said initially it was about August's health and trying to help him heal.

As for August's claim, Will gave Jada his blessing ... that's not the case because the only person that could give permission is Jada herself and, remember, she and Will were separated. Near the end of their convo, Jada said she never felt this was a transgression, either.

They laughed and even invoked one of Will's famous lines when they said, in unison, "We ride together, we die together. Bad marriage for life."

As we reported ... August not long ago sat down with The Breakfast Club's Angela Yee and said he had been in a relationship with Jada after being introduced to her by her son, Jaden, in 2015. August said it lasted quite some time.