<p> Commutative semigroup equations are described, and rules of inference for them are given. Then a skeleton sublattice of the lattice of equational classes of commutative semigroups is described, and a partial description is given of the way in which the rest of the lattice hangs on the skeleton.</p> / Thesis / Doctor of Philosophy (PhD)

<p> In this thesis, we study the concept of injectivity in equational classes of (universal) algebras and in particular we are concerned with congruence distributive equational classes that have enough injectives. We show that every reasonable equationally complete congruence distributive equational class has enough injectives and we describe them completely. We then examine what equational subclasses of Lattices, Heyting algebras, and pseudo-complemented lattices have enough injectives.</p> / Thesis / Doctor of Philosophy (PhD)

The lattice of equational classes of idempotent semigroups is completely described. It is shown that every equational class of idempotent semigroups is determined by a single equation (in addition to the associative and idempotent equations). A method is presented for finding which class a given equation determines, and when the class determined by one equation is contained in the class determined by a second equation. / Thesis / Doctor of Philosophy (PhD)