's oldest son -- who appeared on the family reality show "Coolio's Rules
" --is locked up in a Nevada jail ... after allegedly teaming up with a Vegas hooker to rob some dude at gunpoint.
TMZ has learned ... 22-year-old Grtis Ivey
(who went by "Artis" on the reality show) ... was arrested on November 14, 2011 for allegedly busting into a Vegas apartment with a gun and forcing the tenant into the bathroom ... while he and a female prostitute named Shantrice Wilkerson
ransacked the place.
But the back story is INSANE.
According to the police report, obtained by TMZ ... Shantrice was trollin' at LAX nightclub at the Luxor on October 26 ... and met a guy named Joseph Hall
... who didn't know she was a call girl.
The two hit it off ... and Wilkerson told him that she had a "dream" of having sex on a pile of money.
Hall asked if $5,000 was OK ... she agreed ... and the two eventually went back to Hall's apartment to grab the cash out of a safe.
According to the report, the two bounced to Wilkerson's pad to do the deed ... but before it went down, Wilkerson asked for money ... and Hall flipped out and left.
But cops say, Wilkerson REMEMBERED where Hall lived ... and brought Grtis to the place 3 days later so they could rob it.
According to the report ... Grtis entered the pad with a gun ... and ordered Hall's rooommate into the bathroom while he and the hooker stole a safe, 2 iPads, 2 laptops, passports, and anything else that wasn't nailed down.
Cops say the roommate was able to identify Coolio's son and the hooker -- and both were arrested on a slew of charges including robbery with a deadly weapon, first degree kidnapping and grand larceny.
Both Grtis and Wilkerson told cops they never brought a gun to the apartment ... and Wilkerson admitted to stealing some of the stuff.
Grtis is being held without bail ... and is due to face a judge on Monday.