  In this paper, we consider the tautological ring containing the extended
Brill-Noether algebraic classes on the normalization of the compactified
Jacobian of a complex nodal projective curve (with one node). This smallest
$\Q$-subalgebra of algebraic classes under algebraic equivalence, stable under
extensions of the maps induced by multiplication maps, Pontrayagin product and
Fourier transform, is shown to be generated by pullback of the Brill-Noether
classes of the Jacobian of the normalized curve and some natural classes.
