On the semigroup of all injective orientation-preserving and order-decreasing partial transformations on a finite chain

AYIK H., AYIK G., DAĞDEVİREN A.

Communications in Algebra, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/00927872.2024.2448248
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Injective transformation, minimum generating sets, nilpotent subsemigroups, order-decreasing, order-preserving, orientation-preserving, rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let (Formula presented.) ((Formula presented.)) be the semigroup consisting of all injective orientation-preserving (order-preserving) and order-decreasing transformations on the finite chain (Formula presented.). For (Formula presented.), let (Formula presented.) and (Formula presented.). In this paper, we find the minimal generating sets, and so the ranks of (Formula presented.) and (Formula presented.). We also consider the nilpotent subsemigroup of (Formula presented.).