The purpose of this paper is to
investigate necessary and sufficient conditions on an algebraic semigroup in order
that it have non-trivial right simple homomorphic images. Relative to this, the
relation between the structure of S and the structure of its right simple homomorphs
is characterized.
The main questions considered are:
(1) What characterizes a right simple (right group) conyuence on a semigroup?
(2) Can the conditions found for question (1) be made minimal in order that a
maximum right simple homomorph occurs?
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