On nilpotent subsemigroups of the order-preserving and decreasing transformation semigroups

YAĞCI M., Korkmaz E.

SEMIGROUP FORUM, vol.101, no.2, pp.486-496, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 101 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1007/s00233-020-10098-2
  • Journal Name: SEMIGROUP FORUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.486-496
  • Keywords: Order-preserving, decreasing transformation, Minimum generating set, Rank, Nilpotent subsemigroup
  • Çukurova University Affiliated: Yes

Abstract

Let C-n be the semigroup of all order-preserving and decreasing transformations on X-n = {1, ... , n} under its natural order, and let N(C-n) be the subsemigroup of all nilpotent elements of C n. In this paper we determine the minimum generating set of N(C-n), and so the rank of N(C-n). Moreover, we investigate the nilpotent subsemigroups of C-n.