We report microwave absorption studies on rings containing two-dimensional electrons. The absorption is measured on single rings with different widths using an optical luminescence technique. The dispersion of the plasmon modes has been determined in the presence of a perpendicular magnetic field. The transformation of two-dimensional plasmons in the disk geometry into plasmons with one-dimensional character in a narrow ring is addressed. Experimental data are compared with theoretical estimates based on a self-consistent solution of the Poisson and hydrodynamic equations.