On the Semigroups of Order-preserving and A-Decreasing Finite Transformations

作     者：Ping Zhao 

作者机构：School of Mathematics and Computer Science Guizhou Normal University Guiyang Guizhou 550001 China Mathematics Teaching & Research Section Guiyang Medical College Guiyang Guizhou 550004 China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2014年第21卷第4期

页      面：653-662页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the Natural Science Fund of Guizhou 

主　　题：transformation order-preserving A-decreasing idempotent rank rank 

摘      要：For n E N, let On be the semigroup of all singular order-preserving mappings on [n] = （1, 2,..., n}. For each nonempty subset A of [n], let On （A） = （a ∈ On： （A k ∈ A） ka ≤ k} be the semigroup of all order-preserving and A-decreasing mappings on [n]. In this paper it is shown that On（A）is an abundant semigroup with n - 1 ＊-classes. Moreover, On（A） is idempotent-generated and its idempotent rank is 2n - 2 - IA／（n}l. Further, it is shown that the rank of On（A） is equal to n - 1 if 1 ∈ A, and it is equal to n otherwise.