DEFEAT OF THE F P2 F CONJECTURE - HUCKABA EXAMPLE

A commutative ring R is FP2F (resp. FPF) provided that all finitely presented (resp. finitely generated) faithful modules generate the category mod-R of all R-modules. A conjecture of the author dating to the middle 1970s states that any FP2F ring R has FP-injective classical quotient ring Q = Q(cl)(R). It was shown by the author (Injective quotient rings. II, Lecture Notes in Pure and Appl. Math., vol. 72, Dekker, New York, 1982, pp. 71-105) that FPF rings R have injective Q and by the author and P. Pillay (Classification of commutative FPF rings, Notas Math., vol. 4, Univ. de Murcia, Murcia, Spain, 1990) that CFP2F local rings (defined below) have FP-injective Q. The counterexample is a difficult example due to Huckaba of a strongly Prufer ring without "Properly A." (A ring with Property A was labelled a McCoy ring by the author.) This counterexample is CFP2F in the sense that every factor ring of R is FP2F.