Preheat oven to 400°F. Cut each sausage into 4 equal lengths, then cut each section lengthwise, but not all the way through, so sausage lies flat.
Combine sauerkraut and mayonnaise in small bowl.
Spread ¼ of sauerkraut mixture on each slice of bread. Lay split sausage on sauerkraut and top with a cheese slice.
Place prepared sandwiches on baking sheet and bake 18-20 minutes or until sausage is hot and cheese is lightly browned. Serve open-face.
Cook's Tip: These sandwiches are easy to turn into an appetizer. Substitute 1 loaf (16 ounces) cocktail rye bread for the regular rye bread. Slice sausage into ¼" slices. Spread each mini bread slice with a small portion of the sauerkraut mixture, top with a sausage slice and small slice of cheese. Bake at 400°F. for 15-18 minutes or until sausage is hot and cheese is lightly browned.