It's recommended to keep between 15 to 20 inches of space between a stove and a refrigerator.
But I've had a refrigerator right next to a stove before in a small apartment so you can place a refrigerator next to a stove without much of a problem.
I lived in that apartment for 5 years and the refrigerator nor the stove had any issues but if I had more space I would space the refrigerator and stove at least 20 inches apart.
I've heard the reason to keep a stove and refrigerator apart from each other is due to safety but I don't know what safety issues there would be other than getting the refrigerator hot from the stove burner.
If you do put the stove at least a foot away from the refrigerator you'll have some more work space.