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Gruson-Jensen Duality for Idempotent Rings

ABSTRACT It is known that if R is a ring with identity, and S and A op are the functor rings associated to the categories Mod(R) and Mod(R op ), respectively, then there is a duality between the categories of finitely presented objects of Mod(S op ) and Mod(A). We prove here this result in a more general case, namely when R is an idempotent ring, not necessarily having an identity, and when the categories Mod(R) of torsionfree and unitary right R-modules and Mod(R op ) of torsionfree and unitary left R-modules are locally finitely presented.