由其对应丛确定的正则半群

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.

On Regular Semigroups Determined by Their Bundles of Correspondences

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(∈), forms the bundle of correspondences of S, denoted by(C(S) ,o, -1, ∈ ), 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≌TOPP. 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 result.