On Strong Semilattices of Some Types of Algebras

Our work in this thesis is deeply influenced by the idea that the class of Clifford semigroups is one of the most convenient classes of semigroups viewed as generalized groups. In the sense that , much of the theory and , hence, applications of groups can be extended smoothly to Clifford semigroups with the same flavor and spirit of the realm of groups. One natuaral reason for this is that Clifford semigroups have that structure theorem of strong sort that turns them into strong vi semilattices of groups. As pointed out in [6], one may expect that the same assertion holds for strong semilattices of other kinds of algebras. Perhaps the first published work that introduced a theory of strong semilattices of (arbitrary) algebras is the paper of Plonka and Romanowska [23]. These "general" strong semilattices of algebras have been known in literature as Plonka sums. A partial group is introduced in [6], (see also [1]) as a characterization of a strong semilattice of groups based on generalizing the notions of the identity and inverses in a group . This was followed by studying various algebraic and categorical (universal) constructions for partial groups viewed as generalized groups , [