Akademik Veri Yönetim Sistemi
Asian-European Journal of Mathematics, 2025 (ESCI, Scopus)
For any positive integer n, let On be the semigroup of all order-preserving full transformations on Xn = {1 < ··· < n}. For any 1 ≤ k ≤ n, let πk ∈ On be the constant map defined by xπk = k for all x ∈ Xn. In this paper, we introduce and study the sets of left, right, and two-sided zero-divisors of πk: Lk = {α ∈ On : αβ = πk for some β ∈ On\{πk}}, Rk = {α ∈ On : γα = πk for some γ ∈ On\{πk}}, and Zk = Lk ∩ Rk. We determine the structures and cardinalities of Lk, Rk and Zk for each 1 ≤ k ≤ n. Furthermore, we compute the ranks of R1, Rn, Z1, Zn and Lk for each 1 ≤ k ≤ n, because these are significant subsemigroups of On.