Abstract :
Let S be a g-monoid with quotient group q(S). Let F( ¯ S) (resp.,
F(S), f(S)) be the S-submodules of q(S) (resp., the fractional ideals of S, the
finitely generated fractional ideals of S). Briefly, set f := f(S), g := F(S), h :=
F( ¯ S), and let {x, y} be a subset of the set {f, g, h} of symbols. For a semistar
operation ? on S, if (E +E1)
? = (E +E2)
? implies E1
? = E2
?
for every E ∈ x
and every E1, E2 ∈ y, then ? is called xy-cancellative. In this paper, we prove
that a gg-cancellative semistar operation need not be fh-cancellative
