Ranks of nilpotent subsemigroups of order-preserving and decreasing transformation semigroups
TURKISH JOURNAL OF MATHEMATICS, vol.45, no.4, pp.1626-1634, 2021 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 45 Issue: 4
- Publication Date: 2021
- Doi Number: 10.3906/mat-2008-19
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.1626-1634
- Keywords: Order-preserving and decreasing transformation, nilpotent subsemigroups, m-potent element, generating set, rank
- Çukurova University Affiliated: Yes
Abstract
Let C-n be the semigroup of all order-preserving and decreasing transformations on X = {1, ..., n} under its natural order, and let N(C-n) be the subsemigroup of all nilpotent elements of C-n. For 1 <= r <= n - 1, let