Some different representations of equality algebras

In this paper, by using the notions of equality algebras, filters, prime filters, maximal filters and other properties of equality algebras, some different representations of equality algebras are investigated. First of all, by maximal and prime filters, we proved Chang’s subdirect representation theorem. Then by using the notion of \(\ell \) $\ell$ -groups, we defined two binary operations on it and showed that they made an equality algebra and investigated that under what condition the converse holds. In addition, ordinal sum of two equality algebras are introduced and by using the notion of simple and subdirectly irreducible equality algebras we proved that a special kind of equality algebra can be ordinal sum of two special subalgebras of it.