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Nicole Kidman 's tried to fly under the radar in Tennessee Thursday after a rough week that saw her file for divorce from Keith Urban ... but she couldn't escape the camera lens of the paparazzi.

TMZ obtained photos of the iconic actress making her first public appearance since her split with Urban and she was clearly trying to keep a low profile.

We caught her in Nashville as she walked to her vehicle, wearing athletic gear and a baseball cap pulled down low with black sunglasses. She also seemed deep in thought. Backgrid

Just like Urban, Nicole's no longer wearing her wedding ring in these pics ... so, it seems safe to say this relationships isn't going to revived -- at least, not easily.

We broke the story ... Nicole and Keith have been livi

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