Listing the subsets of Xn to build a (minimal) quasi-idempotent generating set of In,r

BUGAY L.

Asian-European Journal of Mathematics, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s1793557124501146
  • Dergi Adı: Asian-European Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: (minimal) generating set, Quasi-idempotent, rank, symmetric inverse semigroup
  • Çukurova Üniversitesi Adresli: Evet

Özet

LetIn be the symmetric inverse semigroup on the finite chain Xn = {1,...,n} and let In,r = {α In:|im(α)|≤ r} for 1 ≤ r ≤ n - 1. A quasi-idempotent element is an element α In with the property that α α2 = α4. In this paper, we obtain a useful method by listing the subsets of Xn to build a (minimal) quasi-idempotent generating set of In,r both as a semigroup and also as an inverse semigroup for n ≥ 2 and 1 ≤ r ≤ n - 1.