Ranks of certain semigroups of transformations with idempotent complement whose restrictions belong to a given semigroup

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BUGAY L., Sönmez R., AYIK H.

Turkish Journal of Mathematics, cilt.48, sa.3, ss.414-422, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.55730/1300-0098.3516
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.414-422
  • Anahtar Kelimeler: idempotent, Partial (full) transformation semigroup, rank, symmetric group, symmetric inverse semigroup
  • Çukurova Üniversitesi Adresli: Evet

Özet

For n ≥ 2, let Pn, In, Tn, and Sn be the partial transformation semigroup, symmetric inverse semigroup, (full) transformation semigroup, and symmetric group on the set Xn = {1, …, n}, respectively. In this paper, we find the ranks of certain subsemigroups of Pn, In, and Tn consisting of transformations with idempotent complement whose restrictions to the set Xm belong to the (possible) semigroup Sm, Im, Tm, or Pm for 1 ≤ m ≤ n − 1.