Scrub beets thoroughly; remove greens and save for another use. Drizzle lightly with olive oil, and place in a roasting pan. Bake, covered with foil, at 400° for 30 minutes or until tender. Rub the skins off beets with a towel, and slice.
Remove any bones from the salmon. Brush with olive oil, and season lightly with salt and pepper. Grill salmon over medium-hot coals on both sides until medium rare (translucent in the center). Drizzle plates with Balsamic Reduction. Top with beet slices and arugula. Cut salmon into serving pieces, and place on plates.