on a Chain Page 1 Semigroup Forum Vol. 58 (1999) 190-206 © 1999 Springer-Verlag New
York Inc. RESEARCH ARTICLE The Monoid of Orientation-preserving Mappings on a Chain …

Abstract Let D_n (\calO_n) be the semigroup of all finite order-decreasing (order-preserving)
full transformations of an n-element chain, and let D(n,r)={α∈D_n:|Imα|≦r\} …

Let⪯ be a preorder on a monoid H with identity 1 H and s be an integer≥ 2. The⪯-height of
an element x∈ H is the supremum of the integers k≥ 1 for which there is a (strictly)⪯ …

Let Xn={1, 2,..., n}. On a partial transformation α: Dom α⊆ Xn→ Im α⊆ Xn of Xn the following
parameters are defined: the breadth or width of α is| Dom α|, the collapse of α is c (α)=|∪ t∈ …

Let 𝒪 𝒫 ℰ n be the monoid of all orientation-preserving and extensive full transformations on
{1, 2,…, n} ordered in the standard way. In this paper, we determine the minimum generating …

The semigroup OT (X) of all order-preserving total transformations of a finite chain X is
known to be regular. We extend this result to subchains of Z; and we characterise when OT …

In 1962 Alzenstat [1] found a presentation for the monoid On of all order-preserving full
transformations of a finite chain. In this work we find a presentation for the monoid OPn …

降序且保序有限部分变换半群的幂等元秩 Page 1 第46卷第4期 Vol.46 No.4 山东大学学报(理学
版) JournalofShandongUniversity(NaturalScience) 2011年4月 Apr.2011 收稿日期:20100426 …

Let 𝒪 𝒫 ℰ n be the monoid of all orientation-preserving and extensive full transformations on
{1,…, n}. In this paper, we compute the rank and the idempotent rank of the ideals of the …

For n∈ N, let OPE n, k be the monoid of all orientation-preserving k-extensive full
transformations on {1,…, n} ordered in the standard way. In this paper, it is shown that OPE …