On congruence compact monoids

A universal algebra is called congruence compact if every family of congrue nce classes with the finite intersection property has a non-empty intersect ion. This paper determines the structure of all right congruence compact mo noids S for which Green's relations J and H coincide. The results are thus sufficiently general to describe, in particular, all congruence compact com mutative monoids and all right congruence compact Clifford inverse monoids.