半格同余的扩张

SEMILATTICE CONGRUENCE EXTENSIONS

本文研究了一般半群的任意子半群上半相同余扩张的问题。证明了，如果Ｔ是半群Ｓ的Ｃ—子半群，则Ｔ上的每个半格同余能唯一地扩张成Ｓ上的半格同余，并且Ｔ上所有的半格同余与Ｓ上所有的半格同余之间存在相同构。当Ｓ是正则半群，那么Ｓ的全子半群Ｔ上每个半格同余能唯一地扩张成Ｓ上的半格同余当且仅当Ｔ是Ｓ的Ｃ—子半群。

Let S be a semigroup.This paper shows that if T is a C-subsemigroup of S,then every semilattice congruence on T can be uniquely extended to a semilattice congruence on S and there exists a lattice isomorphism from the set of all semilattice congruences on T onto the set of all semilattice congruences on S. It is also proved that if S is a regular semigroup,then for any full subsemigroup T of S,every semilattice congruence on T can be uniquely extended to a semilattice congruence on S if and only if T is a C-subsemigroup of S.