Metalloproteinase inhibitors, pharmaceutical compositions containing them and their pharmaceutical uses

Compounds of formula (I), wherein Y is O or S, Ar is an aryl group or a heteroaryl group, R is H, an alkyl group, a cycloalkyl group, a heterocycloalkyl group, an aryl group, a heteroaryl group, or -C(O)R1, wherein R1 is hydrogen, an alkyl group, a cycloalkyl group, a heterocycloalkyl group, an aryl group, a heteroaryl group, or NR2R3 wherein R2 and R3 independently are hydrogen, an alkyl group, a cycloalkyl group, a heterocycloalkyl group, an aryl group, or a heteroaryl group, and X is -NH-OH or -OH. Pharmaceutically acceptable prodrugs, salts and solvates of these compounds. Methods of inhibiting the activity of metalloproteinases by administering a compound of the formula (I) or a prodrug, salt of solvate thereof. Pharmaceutical compositions comprising an effective amount of these compounds, prodrugs, salts, and solvates.