  The notion of $2$-almost Gorenstein ring is a generalization of the notion of
almost Gorenstein ring in terms of Sally modules of canonical ideals. In this
paper, we deal with two different topics related to $2$-almost Gorenstein
rings. The purposes are to determine all the Ulrich ideals in $2$-almost
Gorenstein rings and to clarify the structure of minimal free resolutions of
$2$-almost Gorenstein rings.
