Is agriculture a proper noun

No, the noun agriculture is a common noun, a general Word for the science or practice of farming; a Word for any type of agriculture anywhere.

A proper noun is the name of a specific person, place, or thing; for example:

• The Honourable Gerry Ritz, Minister of Agriculture and Agri-Food, Canada
• La politique Agricole Commune (PAC) or The Common Agricultural Policy of the European Union
• New York State Department of Agriculture & Markets, Albany, NY