On isolated subsemigroups of order-decreasing transformation semigroups

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Yağcı M., AYIK H.

Hacettepe Journal of Mathematics and Statistics, cilt.55, sa.1, ss.108-116, 2026 (SCI-Expanded, Scopus, TRDizin)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 55 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.15672/hujms.1632145
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.108-116
  • Anahtar Kelimeler: (completely) isolated subsemigroup, convex subsemigroup, generating set, order-decreasing transformation, rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

For n ∈ 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} ̸= U ⊂ Xn which contains 1, we find the rank of Dn [U] = {α ∈ Dn: U ⊆ Xn } which is a convex subsemigroup of Dn .