%A LIU Zu-hua, GUO Yu-qi %T The concatenation of thin languages and r-disjunctive languages ——several studies on combinatorial semigroups(Ⅰ) %0 Journal Article %D 2019 %J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) %R 10.6040/j.issn.1671-9352.0.2019.172 %P 2-7 %V 54 %N 6 %U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3086.shtml} %8 %X The background of this paper is from [1] and another paper(1) by Guo et al., we merge some results in above two papers as Proposition 1: L1L∈Df(Dt, Dr)implies L∈Df(Dt, Dr), where L1,L are languages over alphabet A and L1 is finite. In this paper, a new and simple proof of Proposition 1 is given for Dr. It is proved that Proposition 1 is also true for D and Di. Replacing “finite” with “thin”, Proposition 1 is true for D, Df and Dt; and some examples are given which show that Proposition 1 is not true for Di and Dr.