The Semigroup of Surjective Transformations on an Infinite Set

• 来源期刊: 代数集刊（英文版）
• 关键词: transformation semigroups surjective transformations Green's relations kernels
• 年，卷（期）: 2019,（1）
• 页码范围: 9-22
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386719000038

摘要

For an infinite set X,denote by Ω(X) the semigroup of all surjective mappings from X to X.We determine Green's relations in Ω(X),show that the kernel (unique minimum ideal) of Ω(X) exists and determine its elements and cardinality.For a countably infinite set X,we describe the elements of Ω(X) for which the D-class and J-class coincide.We compare the results for Ω(X) with the corresponding results for other transformation semigroups on X.