On the maximal subsemigroups and relative ranks of certain ideals of finite monotone and order-decreasing partial transformations

AYIK H., AYIK G., Dimitrova I., Koppitz J.

Asian-European Journal of Mathematics, 2026 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1142/s1793557126500579
  • Dergi Adı: Asian-European Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: generating set, maximal subsemigroup, monotone, order-decreasing, order-preserving, order-reversing, partial injective transformation, Partial transformation, rank, relative rank
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let PMDn be the semigroup consisting of all monotone and order-decreasing partial transformations, and let PCn be the subsemigroup of PMDn consisting of all order-preserving and order-decreasing partial transformations on the finite chain (Formula presented). In this paper, we determine the maximal subsemigroups of PMD(n,r), and moreover, we show that the smallest number of elements of PMD(n,r) which, together with PC(n,r), generate PMD(n,r) is n − 2 for every 2 ≤ r ≤ n.