Some Studies Of Congruences On Semigroups

This thesis is mainly devoted to study congruences on regular semigroups, even-tually regular semigroups and E-inversive semigroups.First, we generalized the kernel-trace congruence pairs and kernel normal sys-tems approach about regular semigroups to P-partial congruence pairs and P-partial kernel normal systems on regular semigroups. we have given the P-partial congru-ence pairs on regular semigroups an abstract characterization and proved that con-gruences on regular semigroups is completely determined by its P-partial congruence pairs. These results generalized congruence theory on regular semigroups of Gomes.Next, we generalized the kernel-trace congruence pairs approach to eventually regular semigroups by using weak inversive, characterized the rectangular group congruences on such eventually regular semigroups by means of kernel-trace con-gruence pairs; Then, we given the structure of the maximum inverse semigroup congruences, determined by a given normal congruences on eventually regular semi-groups; We given P-partial kernel normal systems for eventually regular semigroups an abstract characterization. We proved that regular congruences on an eventually regular semigroups is uniquely determined by its P-partial kernel normal systems.Finally, We introduced the definitions of self-conjugate, closed, full subsemi-groups for E-inversive semigroups, proved that group congruences on E-inversive semigroups is uniquely determined by such self-conjugate, closed, full subsemigroups; Then we introduced the definitions of P-partial congruence pairs and P-partial ker-nel normal systems for E-inversive semigroups and an abstract characterization for them obtained. We proved that regular congruences on E-inversive semigroups is uniquely determined by P-partial congruence pairs and P-partial kernel normal sys-tems.