2018 Volume 50 Pages 1-4
Let R be an integral domain with quotient field K, let h (resp., g, f) be the non-zero R-submodules of K (resp., the non-zero fractional ideals of R, the finitely generated non-zero fractional ideals of R), and let {x, y} be a subset of the set {f, g, h} of symbols. For a semistar operation ★ on R, if (EE1)★ = (EE2)★ implies E1★ = E2★ for every E ∈ x and every E1, E2 ∈ y, then ★ is called xy-cancellative. Let ★ be a gg-cancellative semistar operation on R which is an extension of a star operation on R. In this paper, we show that ★ need not be gh-cancellative.