Finite presentablity of some semigroup constructions

In this study, we investigated whether S/p is finite presentable or not where S is a semigroup and p is a congruence on S. We consider p as a subsemigroup of the semigroup of direct product SxS. We showed that S and S/p is finite presentable if p finite presentable as a semigroup. In addition, we construct a presentations for S and S/p from a given presentation of p. Let I be a semilattice, let S(i) be a family of disjoint semigroups, and let S be a strong semilattice of S(i). We construct presentations for S(i) if a presentation for S is given, and a presentation for S if presentations for S(i) are given. Moreover, we investigated the conditions for finite presentability for these presentations. Finally, finite presentability of unions of semigroups, bands of semigroups, bands of monoids and semilattices of semigroups are investigated.