E-inversion Semigroup On Strong After All, Is Pure Congruence And Strong Congruence

In this paper, we mainly study strongly eventually regular congruences, strongly orthodox congruences on an E-inversive semigroup. It is composed of four sections.The first section is a brief introduction and the basic concepts and nec-essary preliminaries.In the second section, some properties of strongly eventually regular con-gruences are given.In the third section, we give relations between a strongly eventually reg-ular congruence and its kernel and trace.In the fourth section, we show that each strongly orthodox congruence on an E-inversive semigroup is uniquely determined by its kernel and hyper-trace. We describe a strongly orthodox congruence on an E-inversive semigroup by means of a strongly orthodox congruence pair.