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Maximal properties of some subsemigroups in finite order-preserving transformation semigroups

 

作者: Yang Xiuliang,   Lu Chunghan,  

 

期刊: Communications in Algebra  （Taylor Available online 2000）
卷期: Volume 28, issue 7  

页码: 3125-3135

 

ISSN:0092-7872

 

年代: 2000

 

DOI:10.1080/00927870008827014

 

出版商: Gordon and Breach Science Publishers Ltd.

 

关键词: finite rransformation semigroup;order-preserving rransformation;maximal idempotent-generated subsemigroup;maximal regular subsemigroup;maximal idempotent-generated regular subsemigroup;20M20

 

数据来源: Taylor

 

摘要:

Let [n] = {1,2,…,n} be a finite set, ordered in the usual way. Theorder-preserving transformation semigroup Onis the set of all order-preserving transformations of [n] (excluding the identity mapping) under composition. In this paper we first describe maximal idempotent-generated subsemigroups ofOn, and show thatOnhas 2n- 2 such subsemi-groups. Secondly, we investigate maximal regular subsemigroups ofOn, and obtain the number of such subsemigroups as 2n- 3. Thirdly, we describe maximal idempotent-generated regular subsemigroups ofOn, and also obtain their classification and number.

 

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