Cher Says Engagement to Alexander Edwards 'Going OK,' Flashes Diamond Ring

Cher and Alexander Edwards' engagement is looking as real as it can be -- they were smiling and playful while hittin' the town together, and showing off her new diamond ring.

The couple was out in Bev Hills Thursday night, heading to Avra for dinner, and couldn't help but do a little smooching -- okay, the paps begged 'em -- during their slow stroll inside the restaurant.

Cher even flashed the shiny new ring she got from AE last month, telling folks their engagement is going along pretty well, too!

As we reported, fans were scratching their heads Christmas day when she shared a massive diamond ring from Alexander with the caption, "THERE R NO WORDS."

Most people weren't sure if it was the real deal, or just some top-shelf trolling.

Cher hasn't been married since Gregg Allman way back in the mid-to-late '70s, and obviously Sonny Bono before that. She's dated a lot since then ... including some heavy hitters like Gene Simmons, Tom Cruise, Val Kilmer, Richie Sambora and Warren Beatty.