Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups

BUGAY L.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, sa.1, ss.281-287, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2001-3
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.281-287
  • Anahtar Kelimeler: Symmetric inverse semigroup, symmetric group, quasi-idempotent, rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let I-n and S-n be the symmetric inverse semigroup and the symmetric group on a finite chain X-n = {1, ... , n}, respectively. Also, let I-n,I- r = {alpha is an element of I-n : |im(alpha)| <= r} for 1 <= r <= n- 1. For any alpha is an element of I-n, if alpha not equal alpha(2) = alpha(4) then a is called a quasi-idempotent. In this paper, we show that the quasi-idempotent rank of In, r (both as a semigroup and as an inverse semigroup) is ( n 2) if r = 2, and ( n r) + 1 if r >= 3. The quasi-idempotent rank of I-n,I- 1 is n (as a semigroup) and n - 1 (as an inverse semigroup).