Yagci, MelekAyik, Hayrullah2026-04-252026-04-2520262651-477Xhttps://doi.org/10.15672/hujms.1632145https://hdl.handle.net/11486/8518For n E N, let Dn be the semigroup of all order-decrasing transformations on Xn = {1, ... , n}, under its natural order. In this paper, we determine isolated, completely isolated, and (left/right) convex subsemigroups of Dn. Furthermore, for {1} =6 U C Xn which contains 1, we find the rank of Dn[U] = {cx E Dn : U C Xn} which is a convex subsemigroup of Dn.eninfo:eu-repo/semantics/openAccessorder-decreasing transformation(completely) isolated subsemigroupconvex subsemigroupgenerating setrankArticle55110811610.15672/hujms.16321452-s2.0-105031280501Q2WOS:001699185100010Q2