Arslan,F.Mete,P.ŞAhin,M.2024-07-052024-07-0520090002-993910.1090/S0002-9939-08-09785-22-s2.0-77951062408https://doi.org/10.1090/S0002-9939-08-09785-2https://hdl.handle.net/20.500.14411/3592In this article, by using the technique of gluing semigroups, we give infinitely many families of 1-dimensional local rings with non-decreasing Hilbert functions. More significantly, these are local rings whose associated graded rings are not necessarily Cohen-Macaulay. In this sense, we give an effective technique for constructing large families of 1-dimensional Gorenstein local rings associated to monomial curves, which support Rossi's conjecture saying that every Gorenstein local ring has a non-decreasing Hilbert function. © 2008 American Mathematical Society.eninfo:eu-repo/semantics/openAccess[No Keyword Available]ArticleQ213772225223223