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Why study abstract algebra? What good is it? The answer to such questions lies, of course, in the questing human intellect that admits no restraints upon its probes. nor limits to its adventures. Utility marches after discovery. The formal systems we are about to study have played important roles in the physical sciences and are of increasing importance in the biological and social sciences. While the algebra may be abstract, it none-theless provides the setting or language for consideration of concrete physical and social problems.