Isolated Subsemigroups of Order-Preserving and Decreasing Transformation Semigroups

KORKMAZ E., AYIK H.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.45, no.2, pp.663-675, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1007/s40840-021-01215-7
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.663-675
  • Keywords: Order-preserving/decreasing transformation, Rank, Nilpotent subsemigroups, Isolated subsemigroups, NILPOTENT SUBSEMIGROUPS, VARIANTS
  • Çukurova University Affiliated: Yes

Abstract

In this paper, we classify all isolated, completely isolated, and (left/right) convex subsemigroups of C-n, the semigroup of all order-preserving and decreasing transformations on X-n = (1, ..., n) under its natural order. Moreover, we find the rank of each convex subsemigroup of C-n.