E-反演半群上的部分核正规系

设S是E-反演半群,P是幂等元集E(S)的一个全子集.介绍了S上P-部分核正规系的概念,证明了S上每个正则同余完全由它的P-部分核正规系惟一确定.然后借助部分核正规系给出核正规系的概念.也给出了由该核正规系所决定的惟一正则同余的一个等价刻画,由此得到S上核正规系的等价刻画.

Partial Kernel Normal System on E-inversive Semigroups

Let S be E-inversive semigroups,P is an full subset of the set E(S) of the idempotents.We first introduce the notion of P-partial kernel normal system on S and prove that each regular congruence on S is uniquely determined by its P-partial kernel normal system.Then the concept of kernel normal system on S is given by means of the concept of the partial kernel normal system.Furthermore,an equivalent characterization of the unique regular congruence determined by this kernel normal system is also given.Therefore an equivalent characterization of kernel normal system on S is obtained.