由其对应丛确定的正则半群(英文)  

On Regular Semigroups Determined by Their Bundles of Correspondences

作　　者：陈建飞[1] 何天荣[1] 

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650031

出　　处：《云南民族大学学报（自然科学版）》2008年第1期1-11,共11页Journal of Yunnan Minzu University:Natural Sciences Edition

摘　　要：设S是一个半群,S×S的所有子半群(含空半群),按照二元关系的复合(o)、逆(-1)及集合包含关系(■)构成了S上的对应丛.记为(C(S),o,-1, )或简记为C(S).如果对任何半群T,只要C(S) C(T),就有S T或S TOPP,则称半群S是C-确定的.Goberstein S M研究了基本逆半群及基本纯整半群的C-确定性.这里主要证明非周期群并的基本正则半群都是C-确定的.Goberstein S M所得到的结论都成为本文所得结果的推论.Given a semigroup S, the set of all subsemigroupe of S × S （ including the empty one）, with the operation of the binary relation composition （o） and natural involution （ - 1 ） and the relation of set-theoretic inclusion（ lohtain in ）, forms the bundle of correspondences of S, denoted by（C（S）,o, -1, lohtain in ）, or shortly by C（S）. S is said to be C-determined if for any semigroup T such that C（S） ≌C（ T）, then S≌T or S≌T^opp. the C-determinability of fundamental inverse semigroups and a special class of fundamental orthodox semigroups have been investigated by Goberstein S M. The main purpose of the present paper is to show that fundamental regular semigroups which are not periodic unions of groups are C-determined. These semigroups form a vast subclass of fundamental regular semigroups. The main results obtained in the above mentioned articles are then deduced easily from this re- suit.

关 键 词：半群的对应丛 双序集 C-同构 基本正则半群 

分 类 号：O187.2[理学—数学]