Amalgamated products of semigroups: the embedding problem
Gerard J. Lallement · Transactions of the American Mathematical Society · 1975
A necessary and sufficient condition for a semigroup amalgam to be embeddable is given. It is in the form of a countable set of equational implications with existential quantifiers. Furthermore it is shown that no finite set of equational implications can serve as a necessary and sufficient condition. Howie’s sufficient condition (see [5]) is derived as a consequence of our main theorem.